identify_processes_colab.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/opherdonchin/BSF_NSF2022/blob/main/identify_processes_colab.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from google.colab import drive\n",
        "drive.mount('/content/drive')\n",
        "data_directory = '/content/drive/MyDrive/Science/BSF Grant - 2022/Data/Simulations'"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dgTK-5L-sZ6G",
        "outputId": "d3a3dc2a-b27e-4ff4-f061-669b4981ddf7"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mounted at /content/drive\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "02POgJnzilu_"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import math\n",
        "import random\n",
        "import pandas as pd\n",
        "import pymc as pm\n",
        "import arviz as az\n",
        "import xarray as xr\n",
        "import os\n",
        "import pickle"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "q9dIJOW_a_3J"
      },
      "source": [
        "# The identification engine (part 1)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vAFMjLYEbGpS"
      },
      "source": [
        "We will first test the identification engine on data built directly from the indentification model rather than using it on data simulated from a learning experiment."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OLYFHmRma9MK"
      },
      "source": [
        "## The model"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lmwOEcyfWJGS"
      },
      "source": [
        "This is supposed to be the identification engine that will take measures of adaptation and skill and attempt to assess how many processes are actually involved. \n",
        "\n",
        "The governing equation from the grant is \n",
        "\n",
        "$$\n",
        "y_{s,m} = \\beta_{0,m} + \\sum_{p=1}^{P}{x_{s,p}\\beta_{p,m}} + \\varepsilon_{s,m}\n",
        "$$\n",
        "\n",
        "Where the symbols mean:\n",
        "- $s$ : subject index\n",
        "- $m$ : measure index\n",
        "- $p$ : hidden process index\n",
        "- $y_{s,m}$ : actual data for subject $s$ in measure $m$\n",
        "- $\\beta_{0,m}$ : mean of measure $m$ across subjects\n",
        "- $x_{s,p}$ : state of process $p$ for subject $s$\n",
        "- $\\beta_{p,m}$ : influence of proccess $p$ on measure $m$\n",
        "- $\\varepsilon_{s,m}$ : noise for individual subject $s$ in measure $m$\n",
        "\n",
        "Of course, for starters we will assume that the noise in measurements is normal (although a $t$ distribution would probably work better), although perhaps some subjects are noisier than others. I'll also assume for now that the measures are normalized from 0 to 1 so that we don't have different variances for each:\n",
        "\n",
        "$$\n",
        "\\varepsilon_{s,m} \\sim \\mathcal{N}(0, \\sigma_s)\n",
        "$$\n",
        "\n",
        "In addition, each subject belongs to an experimental group $g(s)$ and we assume that the subjects in that group have similar engagements in each of the different processes:\n",
        "\n",
        "$$\n",
        "x_{s,p} \\sim \\mathcal{N}(\\mu_{g(s), p}, \\sigma_p)\n",
        "$$\n",
        "\n",
        "The full model inclues a modulation of the effects of a process ($\\beta_{p,m}$) by reward, but we'll leave that out for now.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ghc8ro0dl6j9"
      },
      "outputs": [],
      "source": [
        "# Let's just assume all of our subjects have the same noise for now\n",
        "sigma_s = 0.01\n",
        "# Similarly, the processes are normalized so that they have the same noise\n",
        "sigma_p = 0.02\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NI2TuviobTsr"
      },
      "source": [
        "## Simulating data from the model"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "McpP_7REdyoC"
      },
      "source": [
        "### Measures and processes"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DtueR8aPb2Pe"
      },
      "source": [
        "In this initial simulation there will be 2 processes: \n",
        "\n",
        "- $sr$ : strategic re-aiming\n",
        "- $rc$ : recalibration\n",
        "\n",
        "And there will be 6 measures, three adaptation measures and three measures of skill:\n",
        "\n",
        "- Measures of adaptation\n",
        "  - $lr$ : learning rate\n",
        "  - $la$ : learning asymptote\n",
        "  - $af$ : aftereffect\n",
        "- Measures of skill: change in the measure across time, actually\n",
        "  - $pr$ : preparation time required\n",
        "  - $gn$ : generalization width\n",
        "  - $fb$ : extent of feedback response"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Ug3G9d34fKmJ"
      },
      "outputs": [],
      "source": [
        "num_processes = 2\n",
        "sr = 0\n",
        "rc = 1\n",
        "num_measures = 6\n",
        "lr = 0\n",
        "la = 1\n",
        "af = 2\n",
        "pr = 3\n",
        "gn = 4\n",
        "fb = 5\n",
        "\n",
        "measure_names = ['lr', 'la', 'af', 'pr', 'gn', 'fb']"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 238
        },
        "id": "-Vrm2wFVl13Y",
        "outputId": "bc42628b-479c-455f-bfcd-68dd9b3eed59"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "      0   sr   rc\n",
              "lr  0.5  0.9  0.1\n",
              "la  0.5  0.3  0.7\n",
              "af  0.5  0.0  1.0\n",
              "pr  0.5  1.0  0.0\n",
              "gn  0.5  0.2  0.8\n",
              "fb  0.5  0.0  1.0"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-c5945acc-7f4e-4402-8ad5-674d5580de10\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>0</th>\n",
              "      <th>sr</th>\n",
              "      <th>rc</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>lr</th>\n",
              "      <td>0.5</td>\n",
              "      <td>0.9</td>\n",
              "      <td>0.1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>la</th>\n",
              "      <td>0.5</td>\n",
              "      <td>0.3</td>\n",
              "      <td>0.7</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>af</th>\n",
              "      <td>0.5</td>\n",
              "      <td>0.0</td>\n",
              "      <td>1.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>pr</th>\n",
              "      <td>0.5</td>\n",
              "      <td>1.0</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>gn</th>\n",
              "      <td>0.5</td>\n",
              "      <td>0.2</td>\n",
              "      <td>0.8</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>fb</th>\n",
              "      <td>0.5</td>\n",
              "      <td>0.0</td>\n",
              "      <td>1.0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-c5945acc-7f4e-4402-8ad5-674d5580de10')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-c5945acc-7f4e-4402-8ad5-674d5580de10 button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-c5945acc-7f4e-4402-8ad5-674d5580de10');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ],
      "source": [
        "#              beta_0   sr     rc\n",
        "beta_vals = [ (0.5,     0.9,   0.1) , # Learning rate\n",
        "              (0.5,     0.3,   0.7) , # Learning asymptote\n",
        "              (0.5,     0.0,   1.0) , # Aftereffect\n",
        "              (0.5,     1.0,   0.0) , # Preparation time improvement\n",
        "              (0.5,     0.2,   0.8) , # Generalization widening\n",
        "              (0.5,     0.0,   1.0) , # Feedback response improving\n",
        "              ]\n",
        "# Create DataFrame object from a list of tuples\n",
        "beta = pd.DataFrame(beta_vals, columns = ['0', 'sr', 'rc'], index=measure_names)\n",
        "beta"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "C05tdB-5d1YT"
      },
      "source": [
        "### Groups"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8-Ya3h1Sd36u"
      },
      "source": [
        "The grant describes 10 groups:\n",
        "- Experiment 1 ($N=60$ pre group)\n",
        "  - Low-PT : low preparation time, reduced $sr$\n",
        "  - High-PT : no special effect\n",
        "- Experiment 2 ($N = 60$ per group)\n",
        "  - Immediate : immediate feedback after movement, no special effect\n",
        "  - Delay : Delay in feedback, reduced $rc$\n",
        "- Experiment 3 ($N=30$ per group)\n",
        "  - NoStrat25, NoStrat75 : Same as Low-PT group of experiment 1\n",
        "  - NoRecal25, NoRecal75 : Same as Delay group of experiment 1\n",
        "  - NoBoth25, NoBoth75 : reduction in both $sr$ and $rc$\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 363
        },
        "id": "oMSNuxa-qSuK",
        "outputId": "23c39a05-ea5c-4680-83d2-90ed561f0fe2"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "             sr    rc\n",
              "LowPT      0.05  0.50\n",
              "HighPT     0.50  0.50\n",
              "Imm        0.50  0.50\n",
              "Delay      0.50  0.05\n",
              "NoStrat25  0.05  0.50\n",
              "NoStrat75  0.05  0.50\n",
              "NoRecal25  0.50  0.05\n",
              "NoRecal75  0.50  0.05\n",
              "NoBoth25   0.05  0.05\n",
              "NoBoth75   0.05  0.05"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-b9cb2c21-2695-48b2-81b3-4bc41829548a\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>sr</th>\n",
              "      <th>rc</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>LowPT</th>\n",
              "      <td>0.05</td>\n",
              "      <td>0.50</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>HighPT</th>\n",
              "      <td>0.50</td>\n",
              "      <td>0.50</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Imm</th>\n",
              "      <td>0.50</td>\n",
              "      <td>0.50</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Delay</th>\n",
              "      <td>0.50</td>\n",
              "      <td>0.05</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>NoStrat25</th>\n",
              "      <td>0.05</td>\n",
              "      <td>0.50</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>NoStrat75</th>\n",
              "      <td>0.05</td>\n",
              "      <td>0.50</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>NoRecal25</th>\n",
              "      <td>0.50</td>\n",
              "      <td>0.05</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>NoRecal75</th>\n",
              "      <td>0.50</td>\n",
              "      <td>0.05</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>NoBoth25</th>\n",
              "      <td>0.05</td>\n",
              "      <td>0.05</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>NoBoth75</th>\n",
              "      <td>0.05</td>\n",
              "      <td>0.05</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-b9cb2c21-2695-48b2-81b3-4bc41829548a')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-b9cb2c21-2695-48b2-81b3-4bc41829548a button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-b9cb2c21-2695-48b2-81b3-4bc41829548a');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ],
      "source": [
        "# mu is the average engagement of each group in each process\n",
        "#              sr     rc\n",
        "group_names = ['LowPT', 'HighPT', 'Imm', 'Delay', 'NoStrat25', 'NoStrat75', 'NoRecal25', 'NoRecal75', 'NoBoth25', 'NoBoth75']\n",
        "mu_vals =   [ (0.05,  0.5)  , # Low-PT\n",
        "              (0.5,   0.5)  , # High-PT\n",
        "              (0.5,   0.5)  , # Immediate\n",
        "              (0.5,   0.05) , # Delay\n",
        "              (0.05,  0.5)  , # NoStrat25\n",
        "              (0.05,  0.5)  , # NoStrat75\n",
        "              (0.5,   0.05) , # NoRecal25\n",
        "              (0.5,   0.05) , # NoRecal75\n",
        "              (0.05,  0.05) , # NoBoth25\n",
        "              (0.05,  0.05) , # NoBoth75             \n",
        "             ]\n",
        "mu = pd.DataFrame(mu_vals, columns = ['sr', 'rc'], index=group_names)\n",
        "mu"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 363
        },
        "id": "2fCv9Ve1wYtJ",
        "outputId": "fe2f1451-16a4-4f1b-9cf9-47f560b5dcec"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "            N\n",
              "LowPT      60\n",
              "HighPT     60\n",
              "Imm        60\n",
              "Delay      60\n",
              "NoStrat25  30\n",
              "NoStrat75  30\n",
              "NoRecal25  30\n",
              "NoRecal75  30\n",
              "NoBoth25   30\n",
              "NoBoth75   30"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-a336615e-582f-42ee-970b-690a8bab65cb\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>N</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>LowPT</th>\n",
              "      <td>60</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>HighPT</th>\n",
              "      <td>60</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Imm</th>\n",
              "      <td>60</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Delay</th>\n",
              "      <td>60</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>NoStrat25</th>\n",
              "      <td>30</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>NoStrat75</th>\n",
              "      <td>30</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>NoRecal25</th>\n",
              "      <td>30</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>NoRecal75</th>\n",
              "      <td>30</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>NoBoth25</th>\n",
              "      <td>30</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>NoBoth75</th>\n",
              "      <td>30</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-a336615e-582f-42ee-970b-690a8bab65cb')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-a336615e-582f-42ee-970b-690a8bab65cb button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-a336615e-582f-42ee-970b-690a8bab65cb');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ],
      "source": [
        "group_N_vals =   [ (60)  , # Low-PT\n",
        "              (60)  , # High-PT\n",
        "              (60)  , # Immediate\n",
        "              (60) , # Delay\n",
        "              (30)  , # NoStrat25\n",
        "              (30)  , # NoStrat75\n",
        "              (30) , # NoRecal25\n",
        "              (30) , # NoRecal75\n",
        "              (30) , # NoBoth25\n",
        "              (30) , # NoBoth75             \n",
        "             ]\n",
        "group_N = pd.DataFrame(group_N_vals, columns = ['N'], index=group_names, dtype=\"int\")\n",
        "group_N"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "N8lMfTZCtNON"
      },
      "source": [
        "## Generate subjects"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 363
        },
        "id": "qHA7cRsHw9DE",
        "outputId": "1be459db-c98e-48f0-aa14-fb407ed50fa2"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "             sr    rc   N\n",
              "LowPT      0.05  0.50  60\n",
              "HighPT     0.50  0.50  60\n",
              "Imm        0.50  0.50  60\n",
              "Delay      0.50  0.05  60\n",
              "NoStrat25  0.05  0.50  30\n",
              "NoStrat75  0.05  0.50  30\n",
              "NoRecal25  0.50  0.05  30\n",
              "NoRecal75  0.50  0.05  30\n",
              "NoBoth25   0.05  0.05  30\n",
              "NoBoth75   0.05  0.05  30"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-1996d2d5-2bd5-4f35-806a-a158ce42e8bd\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>sr</th>\n",
              "      <th>rc</th>\n",
              "      <th>N</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>LowPT</th>\n",
              "      <td>0.05</td>\n",
              "      <td>0.50</td>\n",
              "      <td>60</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>HighPT</th>\n",
              "      <td>0.50</td>\n",
              "      <td>0.50</td>\n",
              "      <td>60</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Imm</th>\n",
              "      <td>0.50</td>\n",
              "      <td>0.50</td>\n",
              "      <td>60</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Delay</th>\n",
              "      <td>0.50</td>\n",
              "      <td>0.05</td>\n",
              "      <td>60</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>NoStrat25</th>\n",
              "      <td>0.05</td>\n",
              "      <td>0.50</td>\n",
              "      <td>30</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>NoStrat75</th>\n",
              "      <td>0.05</td>\n",
              "      <td>0.50</td>\n",
              "      <td>30</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>NoRecal25</th>\n",
              "      <td>0.50</td>\n",
              "      <td>0.05</td>\n",
              "      <td>30</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>NoRecal75</th>\n",
              "      <td>0.50</td>\n",
              "      <td>0.05</td>\n",
              "      <td>30</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>NoBoth25</th>\n",
              "      <td>0.05</td>\n",
              "      <td>0.05</td>\n",
              "      <td>30</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>NoBoth75</th>\n",
              "      <td>0.05</td>\n",
              "      <td>0.05</td>\n",
              "      <td>30</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-1996d2d5-2bd5-4f35-806a-a158ce42e8bd')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-1996d2d5-2bd5-4f35-806a-a158ce42e8bd button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-1996d2d5-2bd5-4f35-806a-a158ce42e8bd');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ],
      "source": [
        "groups = pd.concat((mu, group_N), axis=1)\n",
        "groups"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Nd5zZHMRxaUp",
        "outputId": "f0dfc651-65b7-41dc-8889-e4e06b3122df"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "           lr        la        af        pr        gn        fb     group\n",
            "0    0.605641  0.873773  1.016019  0.569937  0.903144  1.010169     LowPT\n",
            "1    0.611339  0.885949  1.006664  0.585318  0.918223  0.997473     LowPT\n",
            "2    0.630398  0.873717  1.025294  0.564826  0.920328  0.977139     LowPT\n",
            "3    0.613175  0.891998  1.002088  0.566276  0.924661  1.022874     LowPT\n",
            "4    0.600158  0.875737  1.008605  0.562907  0.885311  1.033146     LowPT\n",
            "..        ...       ...       ...       ...       ...       ...       ...\n",
            "415  0.557392  0.565421  0.581109  0.542793  0.584379  0.568402  NoBoth75\n",
            "416  0.552741  0.571142  0.582979  0.541075  0.575942  0.567445  NoBoth75\n",
            "417  0.556334  0.562875  0.585627  0.559022  0.592586  0.590445  NoBoth75\n",
            "418  0.574495  0.595750  0.600054  0.562739  0.583116  0.575080  NoBoth75\n",
            "419  0.537522  0.566417  0.574977  0.560970  0.564747  0.581327  NoBoth75\n",
            "\n",
            "[420 rows x 7 columns]\n"
          ]
        }
      ],
      "source": [
        "y_columns = measure_names+['group']\n",
        "y = pd.DataFrame(columns=y_columns)\n",
        "for gp in groups.itertuples():\n",
        "  sr = random.normalvariate(gp.sr, sigma_p)\n",
        "  rc = random.normalvariate(gp.rc, sigma_p)\n",
        "\n",
        "  this_x =pd.DataFrame({\"0\": [1]*gp.N, \"sr\": sr, \"rc\": rc})\n",
        "  these_measures = np.random.normal(loc=this_x.dot( beta.T ), scale=sigma_s)\n",
        "  these_measures = pd.DataFrame(these_measures, columns=measure_names)\n",
        "  these_measures['group'] = gp.Index\n",
        "  y = pd.concat([y,these_measures], ignore_index=True)\n",
        "\n",
        "from pandas.api.types import CategoricalDtype\n",
        "y['group'] = y['group'].astype(CategoricalDtype(categories=group_names))\n",
        "\n",
        "print(y)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-uahxvakbWZk"
      },
      "source": [
        "## Build PyMC model"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "09q5TB-ARGgQ"
      },
      "source": [
        "### Reparameterization of gamma distribution"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IOzn-m1wMHbO"
      },
      "source": [
        "I never remember the formula for parameter transformation for the Gamma distribution. To match the PyMC documentation, we use $\\alpha$ for the shape parameter and $\\beta$ for the rate parameter.\n",
        "\n",
        "If $\\alpha \\ge 1$:\n",
        "$$\n",
        "m = \\frac{\\alpha - 1}{\\beta} \\\\\n",
        "v = \\frac{\\alpha}{\\beta^2}\n",
        "$$\n",
        "So:\n",
        "$$\n",
        "\\alpha = v \\beta^2 \\\\\n",
        "m = \\frac{v \\beta^2 - 1}{\\beta} \\\\\n",
        "m \\beta = v\\beta^2 - 1 \\\\\n",
        "0 = v \\beta^2 - m \\beta -1 \\\\\n",
        "\\beta = \\frac{m + \\sqrt{m^2 + 4 v}}{2v}\n",
        "$$\n",
        "And\n",
        "$$\n",
        "\\alpha = 1+m\\beta\n",
        "$$\n",
        "Note that this means there is a Gamma distribution regardless of your choice of mode and variance (as long as both are positive or 0).\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "FFhuilwZKly6"
      },
      "outputs": [],
      "source": [
        "def gamma_mv2sr(m, v):\n",
        "  r = (m + np.sqrt(m*m + 4*v)) / (2*v)\n",
        "  s = 1 + m*r\n",
        "  return (s, r)\n",
        "\n",
        "def gamma_sr2mv(s,r):\n",
        "  if s>1:\n",
        "    m = (s-1) / r\n",
        "  else:\n",
        "    m = 0\n",
        "  v = s / r^2\n",
        "  return (m,v)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DuHPYjK9RP3T"
      },
      "source": [
        "### Prior parameters"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "fwUHtraKRRx4"
      },
      "outputs": [],
      "source": [
        "sigma_p_mode = 0.5\n",
        "sigma_p_s = 0.5\n",
        "sigma_y_mode = 0.5\n",
        "sigma_y_s = 0.5\n",
        "beta_0_mu = 0.5\n",
        "beta_0_s = 1\n",
        "beta_mu = 0\n",
        "beta_s = 1.5\n",
        "mu_g_mu = 0.5\n",
        "mu_g_s = 1.0"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CXZV9YArRfii"
      },
      "source": [
        "### Define model"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "rkcqAC9LRbSU",
        "outputId": "e42ee203-4b63-485e-d2f0-e8487f9aac61",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(420, 7)\n",
            "lr    0.814070\n",
            "la    0.807428\n",
            "af    0.804132\n",
            "pr    0.815686\n",
            "gn    0.806176\n",
            "fb    0.803902\n",
            "dtype: float64\n",
            "lr    0.198647\n",
            "la    0.152713\n",
            "af    0.218251\n",
            "pr    0.225608\n",
            "gn    0.169770\n",
            "fb    0.218567\n",
            "dtype: float64\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:2: FutureWarning: Dropping of nuisance columns in DataFrame reductions (with 'numeric_only=None') is deprecated; in a future version this will raise TypeError.  Select only valid columns before calling the reduction.\n",
            "  \n",
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:3: FutureWarning: Dropping of nuisance columns in DataFrame reductions (with 'numeric_only=None') is deprecated; in a future version this will raise TypeError.  Select only valid columns before calling the reduction.\n",
            "  This is separate from the ipykernel package so we can avoid doing imports until\n"
          ]
        }
      ],
      "source": [
        "print(y.shape)\n",
        "print(y.mean(axis=0))\n",
        "print(y.std(axis=0))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "nsdkZC9-WIA_"
      },
      "outputs": [],
      "source": [
        "def latent_variable_model(y,groups,P):\n",
        "  gp_idx = groups.cat.codes\n",
        "  group_list = groups.cat.categories\n",
        "  s_idx, subject_list = pd.factorize(y.index)\n",
        "  m_idx, measure_list = pd.factorize(y.columns)\n",
        "\n",
        "  sigma_p_shape, sigma_p_rate = gamma_mv2sr(sigma_p_mode, sigma_p_s*sigma_p_s)\n",
        "  sigma_y_shape, sigma_y_rate = gamma_mv2sr(sigma_y_mode, sigma_y_s*sigma_y_s)\n",
        "\n",
        "  coords = {'subject': subject_list, 'measure': measure_list, 'group':group_list, 'process': range(P)}\n",
        "  with pm.Model(coords=coords) as model:\n",
        "    # Priors\n",
        "    sigma_p = pm.Gamma(\"sigma_p\", alpha=sigma_p_shape, beta=sigma_p_rate)\n",
        "    sigma_y = pm.Gamma(\"sigma_y\", alpha=sigma_y_shape, beta=sigma_y_rate)\n",
        "    beta = pm.Normal('beta', mu=beta_mu, sigma=sigma_p, transform=pm.distributions.transforms.simplex, dims=['process', 'measure'])\n",
        "    mu_g = pm.Normal('mu_g', mu=mu_g_mu, sigma=mu_g_s, dims=['group', 'process'])\n",
        "    # Latent variables\n",
        "    # x = pm.Normal('x', mu=mu_g[gp_idx,:], sigma=sigma_p, dims=['subject', 'process'])\n",
        "    x = pm.Deterministic('x', mu_g[gp_idx,:], dims=['subject', 'process'])\n",
        "    mu_y = pm.Deterministic('mu_y', pm.math.dot(x,beta), dims=['subject', 'measure'])\n",
        "\n",
        "    # Likelihood \n",
        "    obs_y = pm.Normal('obs_y', mu=mu_y, sigma=sigma_y, observed=y, dims=['subject', 'measure'])\n",
        "  return model"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 668
        },
        "id": "noWulVvP0wRs",
        "outputId": "00f29f67-772d-423c-fdaf-01e72bcead6d"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<graphviz.dot.Digraph at 0x7fb32070a1d0>"
            ],
            "image/svg+xml": "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<!-- Generated by graphviz version 2.40.1 (20161225.0304)\n -->\n<!-- Title: %3 Pages: 1 -->\n<svg width=\"362pt\" height=\"485pt\"\n viewBox=\"0.00 0.00 362.00 484.81\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 480.8133)\">\n<title>%3</title>\n<polygon fill=\"#ffffff\" stroke=\"transparent\" points=\"-4,4 -4,-480.8133 358,-480.8133 358,4 -4,4\"/>\n<g id=\"clust1\" class=\"cluster\">\n<title>clusterprocess (2) x measure (6)</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M20,-232.9066C20,-232.9066 157,-232.9066 157,-232.9066 163,-232.9066 169,-238.9066 169,-244.9066 169,-244.9066 169,-334.86 169,-334.86 169,-340.86 163,-346.86 157,-346.86 157,-346.86 20,-346.86 20,-346.86 14,-346.86 8,-340.86 8,-334.86 8,-334.86 8,-244.9066 8,-244.9066 8,-238.9066 14,-232.9066 20,-232.9066\"/>\n<text text-anchor=\"middle\" x=\"88.5\" y=\"-240.7066\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">process (2) x measure (6)</text>\n</g>\n<g id=\"clust2\" class=\"cluster\">\n<title>clustergroup (10) x process (2)</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M189,-354.86C189,-354.86 321,-354.86 321,-354.86 327,-354.86 333,-360.86 333,-366.86 333,-366.86 333,-456.8133 333,-456.8133 333,-462.8133 327,-468.8133 321,-468.8133 321,-468.8133 189,-468.8133 189,-468.8133 183,-468.8133 177,-462.8133 177,-456.8133 177,-456.8133 177,-366.86 177,-366.86 177,-360.86 183,-354.86 189,-354.86\"/>\n<text text-anchor=\"middle\" x=\"255\" y=\"-362.66\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">group (10) x process (2)</text>\n</g>\n<g id=\"clust3\" class=\"cluster\">\n<title>clustersubject (420) x process (2)</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M189,-243.8833C189,-243.8833 334,-243.8833 334,-243.8833 340,-243.8833 346,-249.8833 346,-255.8833 346,-255.8833 346,-323.8833 346,-323.8833 346,-329.8833 340,-335.8833 334,-335.8833 334,-335.8833 189,-335.8833 189,-335.8833 183,-335.8833 177,-329.8833 177,-323.8833 177,-323.8833 177,-255.8833 177,-255.8833 177,-249.8833 183,-243.8833 189,-243.8833\"/>\n<text text-anchor=\"middle\" x=\"261.5\" y=\"-251.6833\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">subject (420) x process (2)</text>\n</g>\n<g id=\"clust4\" class=\"cluster\">\n<title>clustersubject (420) x measure (6)</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M131,-8C131,-8 280,-8 280,-8 286,-8 292,-14 292,-20 292,-20 292,-209.93 292,-209.93 292,-215.93 286,-221.93 280,-221.93 280,-221.93 131,-221.93 131,-221.93 125,-221.93 119,-215.93 119,-209.93 119,-209.93 119,-20 119,-20 119,-14 125,-8 131,-8\"/>\n<text text-anchor=\"middle\" x=\"205.5\" y=\"-15.8\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">subject (420) x measure (6)</text>\n</g>\n<!-- sigma_y -->\n<g id=\"node1\" class=\"node\">\n<title>sigma_y</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"64\" cy=\"-187.43\" rx=\"45.9239\" ry=\"37.4533\"/>\n<text text-anchor=\"middle\" x=\"64\" y=\"-198.73\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">sigma_y</text>\n<text text-anchor=\"middle\" x=\"64\" y=\"-183.73\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">~</text>\n<text text-anchor=\"middle\" x=\"64\" y=\"-168.73\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Gamma</text>\n</g>\n<!-- obs_y -->\n<g id=\"node7\" class=\"node\">\n<title>obs_y</title>\n<ellipse fill=\"#d3d3d3\" stroke=\"#000000\" cx=\"171\" cy=\"-76.4767\" rx=\"42.3529\" ry=\"37.4533\"/>\n<text text-anchor=\"middle\" x=\"171\" y=\"-87.7767\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">obs_y</text>\n<text text-anchor=\"middle\" x=\"171\" y=\"-72.7767\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">~</text>\n<text text-anchor=\"middle\" x=\"171\" y=\"-57.7767\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Normal</text>\n</g>\n<!-- sigma_y&#45;&gt;obs_y -->\n<g id=\"edge6\" class=\"edge\">\n<title>sigma_y&#45;&gt;obs_y</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M92.674,-157.6965C106.0636,-143.8122 122.1189,-127.1638 136.198,-112.5645\"/>\n<polygon fill=\"#000000\" stroke=\"#000000\" points=\"138.9334,-114.7701 143.3557,-105.1423 133.8947,-109.9109 138.9334,-114.7701\"/>\n</g>\n<!-- sigma_p -->\n<g id=\"node2\" class=\"node\">\n<title>sigma_p</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"119\" cy=\"-423.3366\" rx=\"45.9239\" ry=\"37.4533\"/>\n<text text-anchor=\"middle\" x=\"119\" y=\"-434.6366\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">sigma_p</text>\n<text text-anchor=\"middle\" x=\"119\" y=\"-419.6366\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">~</text>\n<text text-anchor=\"middle\" x=\"119\" y=\"-404.6366\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Gamma</text>\n</g>\n<!-- beta -->\n<g id=\"node3\" class=\"node\">\n<title>beta</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"119\" cy=\"-301.3833\" rx=\"42.3529\" ry=\"37.4533\"/>\n<text text-anchor=\"middle\" x=\"119\" y=\"-312.6833\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">beta</text>\n<text text-anchor=\"middle\" x=\"119\" y=\"-297.6833\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">~</text>\n<text text-anchor=\"middle\" x=\"119\" y=\"-282.6833\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Normal</text>\n</g>\n<!-- sigma_p&#45;&gt;beta -->\n<g id=\"edge1\" class=\"edge\">\n<title>sigma_p&#45;&gt;beta</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M119,-385.7515C119,-374.1601 119,-361.2394 119,-349.0625\"/>\n<polygon fill=\"#000000\" stroke=\"#000000\" points=\"122.5001,-349.0542 119,-339.0542 115.5001,-349.0543 122.5001,-349.0542\"/>\n</g>\n<!-- mu_y -->\n<g id=\"node6\" class=\"node\">\n<title>mu_y</title>\n<polygon fill=\"none\" stroke=\"#000000\" points=\"220,-213.93 128,-213.93 128,-160.93 220,-160.93 220,-213.93\"/>\n<text text-anchor=\"middle\" x=\"174\" y=\"-198.73\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mu_y</text>\n<text text-anchor=\"middle\" x=\"174\" y=\"-183.73\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">~</text>\n<text text-anchor=\"middle\" x=\"174\" y=\"-168.73\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Deterministic</text>\n</g>\n<!-- beta&#45;&gt;mu_y -->\n<g id=\"edge4\" class=\"edge\">\n<title>beta&#45;&gt;mu_y</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M135.6511,-266.8843C142.2788,-253.1525 149.9078,-237.3462 156.6071,-223.4659\"/>\n<polygon fill=\"#000000\" stroke=\"#000000\" points=\"159.8782,-224.7406 161.0729,-214.2133 153.5741,-221.6979 159.8782,-224.7406\"/>\n</g>\n<!-- mu_g -->\n<g id=\"node4\" class=\"node\">\n<title>mu_g</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"231\" cy=\"-423.3366\" rx=\"42.3529\" ry=\"37.4533\"/>\n<text text-anchor=\"middle\" x=\"231\" y=\"-434.6366\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">mu_g</text>\n<text text-anchor=\"middle\" x=\"231\" y=\"-419.6366\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">~</text>\n<text text-anchor=\"middle\" x=\"231\" y=\"-404.6366\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Normal</text>\n</g>\n<!-- x -->\n<g id=\"node5\" class=\"node\">\n<title>x</title>\n<polygon fill=\"none\" stroke=\"#000000\" points=\"277,-327.8833 185,-327.8833 185,-274.8833 277,-274.8833 277,-327.8833\"/>\n<text text-anchor=\"middle\" x=\"231\" y=\"-312.6833\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">x</text>\n<text text-anchor=\"middle\" x=\"231\" y=\"-297.6833\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">~</text>\n<text text-anchor=\"middle\" x=\"231\" y=\"-282.6833\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Deterministic</text>\n</g>\n<!-- mu_g&#45;&gt;x -->\n<g id=\"edge2\" class=\"edge\">\n<title>mu_g&#45;&gt;x</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M231,-385.7515C231,-370.7712 231,-353.5709 231,-338.6249\"/>\n<polygon fill=\"#000000\" stroke=\"#000000\" points=\"234.5001,-338.2042 231,-328.2042 227.5001,-338.2043 234.5001,-338.2042\"/>\n</g>\n<!-- x&#45;&gt;mu_y -->\n<g id=\"edge3\" class=\"edge\">\n<title>x&#45;&gt;mu_y</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M217.636,-274.6663C209.9892,-259.3788 200.2943,-239.997 191.9859,-223.3871\"/>\n<polygon fill=\"#000000\" stroke=\"#000000\" points=\"194.8841,-221.3574 187.2802,-213.9796 188.6237,-224.4889 194.8841,-221.3574\"/>\n</g>\n<!-- mu_y&#45;&gt;obs_y -->\n<g id=\"edge5\" class=\"edge\">\n<title>mu_y&#45;&gt;obs_y</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M173.2814,-160.8539C172.9862,-149.9351 172.6349,-136.944 172.2976,-124.4675\"/>\n<polygon fill=\"#000000\" stroke=\"#000000\" points=\"175.7881,-124.0667 172.019,-114.165 168.7907,-124.2559 175.7881,-124.0667\"/>\n</g>\n</g>\n</svg>\n"
          },
          "metadata": {},
          "execution_count": 17
        }
      ],
      "source": [
        "model_processes = 2\n",
        "model = latent_variable_model(y.drop('group',axis=1), y['group'], model_processes)\n",
        "pm.model_to_graphviz(model)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 675
        },
        "id": "GDX1sqiL6I2j",
        "outputId": "dcaa2a98-f21e-43bf-e723-e1eac44bfa29"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "WARNING:aesara.tensor.blas:We did not find a dynamic library in the library_dir of the library we use for blas. If you use ATLAS, make sure to compile it with dynamics library.\n"
          ]
        },
        {
          "output_type": "error",
          "ename": "ValueError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/aesara/compile/function/types.py\u001b[0m in \u001b[0;36m__call__\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n\u001b[1;32m    975\u001b[0m                 \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvm\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 976\u001b[0;31m                 \u001b[0;32mif\u001b[0m \u001b[0moutput_subset\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    977\u001b[0m                 \u001b[0;32melse\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvm\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0moutput_subset\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0moutput_subset\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mValueError\u001b[0m: Input dimension mismatch. One other input has shape[1] = 6, but input[7].shape[1] = 2.",
            "\nDuring handling of the above exception, another exception occurred:\n",
            "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-18-b3199cdd1a65>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mos\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpath\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0misfile\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfit_filename\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m   \u001b[0;32mwith\u001b[0m \u001b[0mmodel\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 6\u001b[0;31m     \u001b[0mfit\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msample\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      7\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      8\u001b[0m   \u001b[0;32mwith\u001b[0m \u001b[0mopen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfit_filename\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'wb'\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mhandle\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/pymc/sampling.py\u001b[0m in \u001b[0;36msample\u001b[0;34m(draws, step, init, n_init, initvals, trace, chain_idx, chains, cores, tune, progressbar, model, random_seed, discard_tuned_samples, compute_convergence_checks, callback, jitter_max_retries, return_inferencedata, idata_kwargs, mp_ctx, **kwargs)\u001b[0m\n\u001b[1;32m    541\u001b[0m             \u001b[0mtune\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mtune\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    542\u001b[0m             \u001b[0minitvals\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0minitvals\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 543\u001b[0;31m             \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    544\u001b[0m         )\n\u001b[1;32m    545\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/pymc/sampling.py\u001b[0m in \u001b[0;36minit_nuts\u001b[0;34m(init, chains, n_init, model, random_seed, progressbar, jitter_max_retries, tune, initvals, **kwargs)\u001b[0m\n\u001b[1;32m   2490\u001b[0m         \u001b[0mseeds\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mrandom_seed_list\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2491\u001b[0m         \u001b[0mjitter\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m\"jitter\"\u001b[0m \u001b[0;32min\u001b[0m \u001b[0minit\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2492\u001b[0;31m         \u001b[0mjitter_max_retries\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mjitter_max_retries\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   2493\u001b[0m     )\n\u001b[1;32m   2494\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/pymc/sampling.py\u001b[0m in \u001b[0;36m_init_jitter\u001b[0;34m(model, initvals, seeds, jitter, jitter_max_retries)\u001b[0m\n\u001b[1;32m   2379\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mi\u001b[0m \u001b[0;34m<\u001b[0m \u001b[0mjitter_max_retries\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2380\u001b[0m                 \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2381\u001b[0;31m                     \u001b[0mmodel\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcheck_start_vals\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpoint\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   2382\u001b[0m                 \u001b[0;32mexcept\u001b[0m \u001b[0mSamplingError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2383\u001b[0m                     \u001b[0;31m# Retry with a new seed\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/pymc/model.py\u001b[0m in \u001b[0;36mcheck_start_vals\u001b[0;34m(self, start)\u001b[0m\n\u001b[1;32m   1789\u001b[0m                 )\n\u001b[1;32m   1790\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1791\u001b[0;31m             \u001b[0minitial_eval\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpoint_logps\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpoint\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0melem\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1792\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1793\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mall\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0misfinite\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mv\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mv\u001b[0m \u001b[0;32min\u001b[0m \u001b[0minitial_eval\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvalues\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/pymc/model.py\u001b[0m in \u001b[0;36mpoint_logps\u001b[0;34m(self, point, round_vals)\u001b[0m\n\u001b[1;32m   1830\u001b[0m             for factor, factor_logp in zip(\n\u001b[1;32m   1831\u001b[0m                 \u001b[0mfactors\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1832\u001b[0;31m                 \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcompile_fn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfactor_logps_fn\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpoint\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1833\u001b[0m             )\n\u001b[1;32m   1834\u001b[0m         }\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/pymc/aesaraf.py\u001b[0m in \u001b[0;36m__call__\u001b[0;34m(self, state)\u001b[0m\n\u001b[1;32m    693\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    694\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m__call__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstate\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 695\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0mstate\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    696\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    697\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/aesara/compile/function/types.py\u001b[0m in \u001b[0;36m__call__\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n\u001b[1;32m    990\u001b[0m                     \u001b[0mnode\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnodes\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mposition_of_error\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    991\u001b[0m                     \u001b[0mthunk\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mthunk\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 992\u001b[0;31m                     \u001b[0mstorage_map\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mgetattr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvm\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"storage_map\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    993\u001b[0m                 )\n\u001b[1;32m    994\u001b[0m             \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/aesara/link/utils.py\u001b[0m in \u001b[0;36mraise_with_op\u001b[0;34m(fgraph, node, thunk, exc_info, storage_map)\u001b[0m\n\u001b[1;32m    532\u001b[0m         \u001b[0;31m# Some exception need extra parameter in inputs. So forget the\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    533\u001b[0m         \u001b[0;31m# extra long error message in that case.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 534\u001b[0;31m     \u001b[0;32mraise\u001b[0m \u001b[0mexc_value\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mwith_traceback\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mexc_trace\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    535\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    536\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/aesara/compile/function/types.py\u001b[0m in \u001b[0;36m__call__\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n\u001b[1;32m    974\u001b[0m             outputs = (\n\u001b[1;32m    975\u001b[0m                 \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvm\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 976\u001b[0;31m                 \u001b[0;32mif\u001b[0m \u001b[0moutput_subset\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    977\u001b[0m                 \u001b[0;32melse\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvm\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0moutput_subset\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0moutput_subset\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    978\u001b[0m             )\n",
            "\u001b[0;31mValueError\u001b[0m: Input dimension mismatch. One other input has shape[1] = 6, but input[7].shape[1] = 2.\nApply node that caused the error: Elemwise{Composite{(Switch(i0, ((i1 + (i2 * sqr((i3 / i4)))) - i5), i6) + i7)}}[(0, 3)](Elemwise{gt,no_inplace}.0, TensorConstant{(1, 1) of ..5332046727}, TensorConstant{(1, 1) of -0.5}, beta_simplex___simplex, InplaceDimShuffle{x,x}.0, InplaceDimShuffle{x,x}.0, TensorConstant{(1, 1) of -inf}, Elemwise{Composite{((i0 + (i1 * i2)) - (i1 * (i3 + log(i4))))}}[(0, 2)].0)\nToposort index: 41\nInputs types: [TensorType(bool, (1, 1)), TensorType(float64, (1, 1)), TensorType(float64, (1, 1)), TensorType(float64, (None, None)), TensorType(float64, (1, 1)), TensorType(float64, (1, 1)), TensorType(float32, (1, 1)), TensorType(float64, (1, None))]\nInputs shapes: [(1, 1), (1, 1), (1, 1), (2, 6), (1, 1), (1, 1), (1, 1), (1, 2)]\nInputs strides: [(1, 1), (8, 8), (8, 8), (48, 8), (8, 8), (8, 8), (4, 4), (16, 8)]\nInputs values: [array([[ True]]), array([[-0.91893853]]), array([[-0.5]]), 'not shown', array([[0.66728827]]), array([[-0.40453314]]), array([[-inf]], dtype=float32), array([[nan, nan]])]\nOutputs clients: [[Sum{acc_dtype=float64}(beta_simplex___logprob)]]\n\nHINT: Re-running with most Aesara optimizations disabled could provide a back-trace showing when this node was created. This can be done by setting the Aesara flag 'optimizer=fast_compile'. If that does not work, Aesara optimizations can be disabled with 'optimizer=None'.\nHINT: Use the Aesara flag `exception_verbosity=high` for a debug print-out and storage map footprint of this Apply node."
          ]
        }
      ],
      "source": [
        "fit_filename = os.path.join(data_directory, f'model_samples_{model_processes}_process_new.pickle')\n",
        "\n",
        "# os.remove(fit_filename)\n",
        "if not os.path.isfile(fit_filename):\n",
        "  with model:\n",
        "    fit = pm.sample()\n",
        "\n",
        "  with open(fit_filename, 'wb') as handle:\n",
        "    pickle.dump(fit, handle, protocol=pickle.HIGHEST_PROTOCOL)\n",
        "  # ds_fit = az.convert_to_dataset(fit)\n",
        "  # ds_fit.to_netcdf(fit_filename, engine=\"scipy\")\n",
        "else:\n",
        "  with open(fit_filename, 'rb') as handle:\n",
        "    fit = pickle.load(handle)  \n",
        "  # ds_fit = xr.open_dataset(fit_filename)\n",
        "  # fit = az.convert_to_inference_data(ds_fit)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "fit"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 161
        },
        "id": "wTzI0UKCv__T",
        "outputId": "3bedf15d-a2ea-484e-a205-7dbc8408accc"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Inference data with groups:\n",
              "\t> posterior\n",
              "\t> log_likelihood\n",
              "\t> sample_stats\n",
              "\t> observed_data"
            ],
            "text/html": [
              "\n",
              "            <div>\n",
              "              <div class='xr-header'>\n",
              "                <div class=\"xr-obj-type\">arviz.InferenceData</div>\n",
              "              </div>\n",
              "              <ul class=\"xr-sections group-sections\">\n",
              "              \n",
              "            <li class = \"xr-section-item\">\n",
              "                  <input id=\"idata_posterior04f613b5-73e1-4aba-adb7-612f3ef13d88\" class=\"xr-section-summary-in\" type=\"checkbox\">\n",
              "                  <label for=\"idata_posterior04f613b5-73e1-4aba-adb7-612f3ef13d88\" class = \"xr-section-summary\">posterior</label>\n",
              "                  <div class=\"xr-section-inline-details\"></div>\n",
              "                  <div class=\"xr-section-details\">\n",
              "                      <ul id=\"xr-dataset-coord-list\" class=\"xr-var-list\">\n",
              "                          <div style=\"padding-left:2rem;\"><div><svg style=\"position: absolute; width: 0; height: 0; overflow: hidden\">\n",
              "<defs>\n",
              "<symbol id=\"icon-database\" viewBox=\"0 0 32 32\">\n",
              "<path d=\"M16 0c-8.837 0-16 2.239-16 5v4c0 2.761 7.163 5 16 5s16-2.239 16-5v-4c0-2.761-7.163-5-16-5z\"></path>\n",
              "<path d=\"M16 17c-8.837 0-16-2.239-16-5v6c0 2.761 7.163 5 16 5s16-2.239 16-5v-6c0 2.761-7.163 5-16 5z\"></path>\n",
              "<path d=\"M16 26c-8.837 0-16-2.239-16-5v6c0 2.761 7.163 5 16 5s16-2.239 16-5v-6c0 2.761-7.163 5-16 5z\"></path>\n",
              "</symbol>\n",
              "<symbol id=\"icon-file-text2\" viewBox=\"0 0 32 32\">\n",
              "<path d=\"M28.681 7.159c-0.694-0.947-1.662-2.053-2.724-3.116s-2.169-2.030-3.116-2.724c-1.612-1.182-2.393-1.319-2.841-1.319h-15.5c-1.378 0-2.5 1.121-2.5 2.5v27c0 1.378 1.122 2.5 2.5 2.5h23c1.378 0 2.5-1.122 2.5-2.5v-19.5c0-0.448-0.137-1.23-1.319-2.841zM24.543 5.457c0.959 0.959 1.712 1.825 2.268 2.543h-4.811v-4.811c0.718 0.556 1.584 1.309 2.543 2.268zM28 29.5c0 0.271-0.229 0.5-0.5 0.5h-23c-0.271 0-0.5-0.229-0.5-0.5v-27c0-0.271 0.229-0.5 0.5-0.5 0 0 15.499-0 15.5 0v7c0 0.552 0.448 1 1 1h7v19.5z\"></path>\n",
              "<path d=\"M23 26h-14c-0.552 0-1-0.448-1-1s0.448-1 1-1h14c0.552 0 1 0.448 1 1s-0.448 1-1 1z\"></path>\n",
              "<path d=\"M23 22h-14c-0.552 0-1-0.448-1-1s0.448-1 1-1h14c0.552 0 1 0.448 1 1s-0.448 1-1 1z\"></path>\n",
              "<path d=\"M23 18h-14c-0.552 0-1-0.448-1-1s0.448-1 1-1h14c0.552 0 1 0.448 1 1s-0.448 1-1 1z\"></path>\n",
              "</symbol>\n",
              "</defs>\n",
              "</svg>\n",
              "<style>/* CSS stylesheet for displaying xarray objects in jupyterlab.\n",
              " *\n",
              " */\n",
              "\n",
              ":root {\n",
              "  --xr-font-color0: var(--jp-content-font-color0, rgba(0, 0, 0, 1));\n",
              "  --xr-font-color2: var(--jp-content-font-color2, rgba(0, 0, 0, 0.54));\n",
              "  --xr-font-color3: var(--jp-content-font-color3, rgba(0, 0, 0, 0.38));\n",
              "  --xr-border-color: var(--jp-border-color2, #e0e0e0);\n",
              "  --xr-disabled-color: var(--jp-layout-color3, #bdbdbd);\n",
              "  --xr-background-color: var(--jp-layout-color0, white);\n",
              "  --xr-background-color-row-even: var(--jp-layout-color1, white);\n",
              "  --xr-background-color-row-odd: var(--jp-layout-color2, #eeeeee);\n",
              "}\n",
              "\n",
              "html[theme=dark],\n",
              "body.vscode-dark {\n",
              "  --xr-font-color0: rgba(255, 255, 255, 1);\n",
              "  --xr-font-color2: rgba(255, 255, 255, 0.54);\n",
              "  --xr-font-color3: rgba(255, 255, 255, 0.38);\n",
              "  --xr-border-color: #1F1F1F;\n",
              "  --xr-disabled-color: #515151;\n",
              "  --xr-background-color: #111111;\n",
              "  --xr-background-color-row-even: #111111;\n",
              "  --xr-background-color-row-odd: #313131;\n",
              "}\n",
              "\n",
              ".xr-wrap {\n",
              "  display: block !important;\n",
              "  min-width: 300px;\n",
              "  max-width: 700px;\n",
              "}\n",
              "\n",
              ".xr-text-repr-fallback {\n",
              "  /* fallback to plain text repr when CSS is not injected (untrusted notebook) */\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-header {\n",
              "  padding-top: 6px;\n",
              "  padding-bottom: 6px;\n",
              "  margin-bottom: 4px;\n",
              "  border-bottom: solid 1px var(--xr-border-color);\n",
              "}\n",
              "\n",
              ".xr-header > div,\n",
              ".xr-header > ul {\n",
              "  display: inline;\n",
              "  margin-top: 0;\n",
              "  margin-bottom: 0;\n",
              "}\n",
              "\n",
              ".xr-obj-type,\n",
              ".xr-array-name {\n",
              "  margin-left: 2px;\n",
              "  margin-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-obj-type {\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-sections {\n",
              "  padding-left: 0 !important;\n",
              "  display: grid;\n",
              "  grid-template-columns: 150px auto auto 1fr 20px 20px;\n",
              "}\n",
              "\n",
              ".xr-section-item {\n",
              "  display: contents;\n",
              "}\n",
              "\n",
              ".xr-section-item input {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-section-item input + label {\n",
              "  color: var(--xr-disabled-color);\n",
              "}\n",
              "\n",
              ".xr-section-item input:enabled + label {\n",
              "  cursor: pointer;\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-section-item input:enabled + label:hover {\n",
              "  color: var(--xr-font-color0);\n",
              "}\n",
              "\n",
              ".xr-section-summary {\n",
              "  grid-column: 1;\n",
              "  color: var(--xr-font-color2);\n",
              "  font-weight: 500;\n",
              "}\n",
              "\n",
              ".xr-section-summary > span {\n",
              "  display: inline-block;\n",
              "  padding-left: 0.5em;\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:disabled + label {\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-section-summary-in + label:before {\n",
              "  display: inline-block;\n",
              "  content: '►';\n",
              "  font-size: 11px;\n",
              "  width: 15px;\n",
              "  text-align: center;\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:disabled + label:before {\n",
              "  color: var(--xr-disabled-color);\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:checked + label:before {\n",
              "  content: '▼';\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:checked + label > span {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-section-summary,\n",
              ".xr-section-inline-details {\n",
              "  padding-top: 4px;\n",
              "  padding-bottom: 4px;\n",
              "}\n",
              "\n",
              ".xr-section-inline-details {\n",
              "  grid-column: 2 / -1;\n",
              "}\n",
              "\n",
              ".xr-section-details {\n",
              "  display: none;\n",
              "  grid-column: 1 / -1;\n",
              "  margin-bottom: 5px;\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:checked ~ .xr-section-details {\n",
              "  display: contents;\n",
              "}\n",
              "\n",
              ".xr-array-wrap {\n",
              "  grid-column: 1 / -1;\n",
              "  display: grid;\n",
              "  grid-template-columns: 20px auto;\n",
              "}\n",
              "\n",
              ".xr-array-wrap > label {\n",
              "  grid-column: 1;\n",
              "  vertical-align: top;\n",
              "}\n",
              "\n",
              ".xr-preview {\n",
              "  color: var(--xr-font-color3);\n",
              "}\n",
              "\n",
              ".xr-array-preview,\n",
              ".xr-array-data {\n",
              "  padding: 0 5px !important;\n",
              "  grid-column: 2;\n",
              "}\n",
              "\n",
              ".xr-array-data,\n",
              ".xr-array-in:checked ~ .xr-array-preview {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-array-in:checked ~ .xr-array-data,\n",
              ".xr-array-preview {\n",
              "  display: inline-block;\n",
              "}\n",
              "\n",
              ".xr-dim-list {\n",
              "  display: inline-block !important;\n",
              "  list-style: none;\n",
              "  padding: 0 !important;\n",
              "  margin: 0;\n",
              "}\n",
              "\n",
              ".xr-dim-list li {\n",
              "  display: inline-block;\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "}\n",
              "\n",
              ".xr-dim-list:before {\n",
              "  content: '(';\n",
              "}\n",
              "\n",
              ".xr-dim-list:after {\n",
              "  content: ')';\n",
              "}\n",
              "\n",
              ".xr-dim-list li:not(:last-child):after {\n",
              "  content: ',';\n",
              "  padding-right: 5px;\n",
              "}\n",
              "\n",
              ".xr-has-index {\n",
              "  font-weight: bold;\n",
              "}\n",
              "\n",
              ".xr-var-list,\n",
              ".xr-var-item {\n",
              "  display: contents;\n",
              "}\n",
              "\n",
              ".xr-var-item > div,\n",
              ".xr-var-item label,\n",
              ".xr-var-item > .xr-var-name span {\n",
              "  background-color: var(--xr-background-color-row-even);\n",
              "  margin-bottom: 0;\n",
              "}\n",
              "\n",
              ".xr-var-item > .xr-var-name:hover span {\n",
              "  padding-right: 5px;\n",
              "}\n",
              "\n",
              ".xr-var-list > li:nth-child(odd) > div,\n",
              ".xr-var-list > li:nth-child(odd) > label,\n",
              ".xr-var-list > li:nth-child(odd) > .xr-var-name span {\n",
              "  background-color: var(--xr-background-color-row-odd);\n",
              "}\n",
              "\n",
              ".xr-var-name {\n",
              "  grid-column: 1;\n",
              "}\n",
              "\n",
              ".xr-var-dims {\n",
              "  grid-column: 2;\n",
              "}\n",
              "\n",
              ".xr-var-dtype {\n",
              "  grid-column: 3;\n",
              "  text-align: right;\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-var-preview {\n",
              "  grid-column: 4;\n",
              "}\n",
              "\n",
              ".xr-var-name,\n",
              ".xr-var-dims,\n",
              ".xr-var-dtype,\n",
              ".xr-preview,\n",
              ".xr-attrs dt {\n",
              "  white-space: nowrap;\n",
              "  overflow: hidden;\n",
              "  text-overflow: ellipsis;\n",
              "  padding-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-var-name:hover,\n",
              ".xr-var-dims:hover,\n",
              ".xr-var-dtype:hover,\n",
              ".xr-attrs dt:hover {\n",
              "  overflow: visible;\n",
              "  width: auto;\n",
              "  z-index: 1;\n",
              "}\n",
              "\n",
              ".xr-var-attrs,\n",
              ".xr-var-data {\n",
              "  display: none;\n",
              "  background-color: var(--xr-background-color) !important;\n",
              "  padding-bottom: 5px !important;\n",
              "}\n",
              "\n",
              ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
              ".xr-var-data-in:checked ~ .xr-var-data {\n",
              "  display: block;\n",
              "}\n",
              "\n",
              ".xr-var-data > table {\n",
              "  float: right;\n",
              "}\n",
              "\n",
              ".xr-var-name span,\n",
              ".xr-var-data,\n",
              ".xr-attrs {\n",
              "  padding-left: 25px !important;\n",
              "}\n",
              "\n",
              ".xr-attrs,\n",
              ".xr-var-attrs,\n",
              ".xr-var-data {\n",
              "  grid-column: 1 / -1;\n",
              "}\n",
              "\n",
              "dl.xr-attrs {\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "  display: grid;\n",
              "  grid-template-columns: 125px auto;\n",
              "}\n",
              "\n",
              ".xr-attrs dt,\n",
              ".xr-attrs dd {\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "  float: left;\n",
              "  padding-right: 10px;\n",
              "  width: auto;\n",
              "}\n",
              "\n",
              ".xr-attrs dt {\n",
              "  font-weight: normal;\n",
              "  grid-column: 1;\n",
              "}\n",
              "\n",
              ".xr-attrs dt:hover span {\n",
              "  display: inline-block;\n",
              "  background: var(--xr-background-color);\n",
              "  padding-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-attrs dd {\n",
              "  grid-column: 2;\n",
              "  white-space: pre-wrap;\n",
              "  word-break: break-all;\n",
              "}\n",
              "\n",
              ".xr-icon-database,\n",
              ".xr-icon-file-text2 {\n",
              "  display: inline-block;\n",
              "  vertical-align: middle;\n",
              "  width: 1em;\n",
              "  height: 1.5em !important;\n",
              "  stroke-width: 0;\n",
              "  stroke: currentColor;\n",
              "  fill: currentColor;\n",
              "}\n",
              "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n",
              "Dimensions:  (chain: 2, draw: 1000, measure: 6, process: 2, group: 10, subject: 420)\n",
              "Coordinates:\n",
              "  * chain    (chain) int64 0 1\n",
              "  * draw     (draw) int64 0 1 2 3 4 5 6 7 8 ... 992 993 994 995 996 997 998 999\n",
              "  * measure  (measure) &lt;U2 &#x27;lr&#x27; &#x27;la&#x27; &#x27;af&#x27; &#x27;pr&#x27; &#x27;gn&#x27; &#x27;fb&#x27;\n",
              "  * process  (process) int64 0 1\n",
              "  * group    (group) &lt;U9 &#x27;Delay&#x27; &#x27;HighPT&#x27; &#x27;Imm&#x27; ... &#x27;NoStrat25&#x27; &#x27;NoStrat75&#x27;\n",
              "  * subject  (subject) int64 0 1 2 3 4 5 6 7 ... 412 413 414 415 416 417 418 419\n",
              "Data variables:\n",
              "    beta_0   (chain, draw, measure) float64 0.765 0.8137 ... 0.9891 0.9971\n",
              "    beta     (chain, draw, process, measure) float64 0.1597 0.1533 ... -0.213\n",
              "    mu_g     (chain, draw, group, process) float64 -0.2125 1.394 ... 0.6707\n",
              "    x        (chain, draw, subject, process) float64 0.05988 -0.9823 ... 1.192\n",
              "    sigma_p  (chain, draw) float64 0.009367 0.009306 ... 0.003321 0.003305\n",
              "    sigma_y  (chain, draw) float64 0.01012 0.00993 0.01001 ... 0.0101 0.01011\n",
              "    mu_y     (chain, draw, subject, measure) float64 0.5966 0.8792 ... 0.5487\n",
              "Attributes:\n",
              "    created_at:                 2022-10-05T04:33:10.841898\n",
              "    arviz_version:              0.12.1\n",
              "    inference_library:          pymc\n",
              "    inference_library_version:  4.1.4\n",
              "    sampling_time:              122.29010105133057\n",
              "    tuning_steps:               1000</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-2c2babbb-a0e7-412b-8431-cb578396cc69' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-2c2babbb-a0e7-412b-8431-cb578396cc69' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>chain</span>: 2</li><li><span class='xr-has-index'>draw</span>: 1000</li><li><span class='xr-has-index'>measure</span>: 6</li><li><span class='xr-has-index'>process</span>: 2</li><li><span class='xr-has-index'>group</span>: 10</li><li><span class='xr-has-index'>subject</span>: 420</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-a4c99f7b-a823-42c7-93fe-d0e8820be29d' class='xr-section-summary-in' type='checkbox'  checked><label for='section-a4c99f7b-a823-42c7-93fe-d0e8820be29d' class='xr-section-summary' >Coordinates: <span>(6)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>chain</span></div><div class='xr-var-dims'>(chain)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1</div><input id='attrs-b5fd3247-e2f3-4b6e-82fd-77e6c8657530' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-b5fd3247-e2f3-4b6e-82fd-77e6c8657530' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-958d78e0-4a7b-49d1-8bbb-4d5c9f0095b8' class='xr-var-data-in' type='checkbox'><label for='data-958d78e0-4a7b-49d1-8bbb-4d5c9f0095b8' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0, 1])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>draw</span></div><div class='xr-var-dims'>(draw)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 5 ... 995 996 997 998 999</div><input id='attrs-76e7ea71-fd66-40ac-9ed0-f5555613496a' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-76e7ea71-fd66-40ac-9ed0-f5555613496a' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-f7902be3-1e7c-4f97-92ec-c322ccb062f8' class='xr-var-data-in' type='checkbox'><label for='data-f7902be3-1e7c-4f97-92ec-c322ccb062f8' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([  0,   1,   2, ..., 997, 998, 999])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>measure</span></div><div class='xr-var-dims'>(measure)</div><div class='xr-var-dtype'>&lt;U2</div><div class='xr-var-preview xr-preview'>&#x27;lr&#x27; &#x27;la&#x27; &#x27;af&#x27; &#x27;pr&#x27; &#x27;gn&#x27; &#x27;fb&#x27;</div><input id='attrs-05634e62-1d2d-4d1e-93ee-6ac8f5fb1d0e' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-05634e62-1d2d-4d1e-93ee-6ac8f5fb1d0e' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-dfcd45ba-cf12-43ab-b2b1-ff28821e3d61' class='xr-var-data-in' type='checkbox'><label for='data-dfcd45ba-cf12-43ab-b2b1-ff28821e3d61' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([&#x27;lr&#x27;, &#x27;la&#x27;, &#x27;af&#x27;, &#x27;pr&#x27;, &#x27;gn&#x27;, &#x27;fb&#x27;], dtype=&#x27;&lt;U2&#x27;)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>process</span></div><div class='xr-var-dims'>(process)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1</div><input id='attrs-6abce8be-e901-4726-a9df-5aa9167dd62a' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-6abce8be-e901-4726-a9df-5aa9167dd62a' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-74239a1a-20be-4da3-9bd0-b3d0dd17da4b' class='xr-var-data-in' type='checkbox'><label for='data-74239a1a-20be-4da3-9bd0-b3d0dd17da4b' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0, 1])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>group</span></div><div class='xr-var-dims'>(group)</div><div class='xr-var-dtype'>&lt;U9</div><div class='xr-var-preview xr-preview'>&#x27;Delay&#x27; &#x27;HighPT&#x27; ... &#x27;NoStrat75&#x27;</div><input id='attrs-b62fe164-f152-48bb-8d04-d4c5da5cc0f8' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-b62fe164-f152-48bb-8d04-d4c5da5cc0f8' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-ea3b47e8-6428-4eee-b738-2e19596111b8' class='xr-var-data-in' type='checkbox'><label for='data-ea3b47e8-6428-4eee-b738-2e19596111b8' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([&#x27;Delay&#x27;, &#x27;HighPT&#x27;, &#x27;Imm&#x27;, &#x27;LowPT&#x27;, &#x27;NoBoth25&#x27;, &#x27;NoBoth75&#x27;, &#x27;NoRecal25&#x27;,\n",
              "       &#x27;NoRecal75&#x27;, &#x27;NoStrat25&#x27;, &#x27;NoStrat75&#x27;], dtype=&#x27;&lt;U9&#x27;)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>subject</span></div><div class='xr-var-dims'>(subject)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 5 ... 415 416 417 418 419</div><input id='attrs-465b4d4b-0937-405b-b558-2d3da1b5880e' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-465b4d4b-0937-405b-b558-2d3da1b5880e' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-b9db02ab-26cd-4f5f-b559-7b8f7f252102' class='xr-var-data-in' type='checkbox'><label for='data-b9db02ab-26cd-4f5f-b559-7b8f7f252102' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([  0,   1,   2, ..., 417, 418, 419])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-d8fc05f5-ad0e-4738-ba9c-7343ce778cf7' class='xr-section-summary-in' type='checkbox'  checked><label for='section-d8fc05f5-ad0e-4738-ba9c-7343ce778cf7' class='xr-section-summary' >Data variables: <span>(7)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>beta_0</span></div><div class='xr-var-dims'>(chain, draw, measure)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.765 0.8137 ... 0.9891 0.9971</div><input id='attrs-4c8a06ea-1a68-4b4e-adbb-7b5d67fb4ea6' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-4c8a06ea-1a68-4b4e-adbb-7b5d67fb4ea6' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-7f1a9efb-b8ae-473d-b1e1-a21482968c8c' class='xr-var-data-in' type='checkbox'><label for='data-7f1a9efb-b8ae-473d-b1e1-a21482968c8c' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[[0.76503242, 0.81369287, 0.83766742, 0.75625497, 0.82072201,\n",
              "         0.83700076],\n",
              "        [0.76336455, 0.81291821, 0.83684849, 0.75618418, 0.82102279,\n",
              "         0.83828207],\n",
              "        [0.76342113, 0.81208767, 0.83708086, 0.75681809, 0.82093744,\n",
              "         0.83606874],\n",
              "        ...,\n",
              "        [0.76807272, 0.81935237, 0.84439008, 0.76021103, 0.82647345,\n",
              "         0.84512283],\n",
              "        [0.76788982, 0.81861229, 0.84474857, 0.75896786, 0.82687655,\n",
              "         0.84506866],\n",
              "        [0.76799368, 0.8187147 , 0.84475996, 0.75864076, 0.8276908 ,\n",
              "         0.84486072]],\n",
              "\n",
              "       [[0.95245774, 0.97909345, 0.99287637, 0.94864834, 0.98238923,\n",
              "         0.99110895],\n",
              "        [0.95058817, 0.97701647, 0.99296487, 0.94636676, 0.98173323,\n",
              "         0.99108021],\n",
              "        [0.95073796, 0.97720795, 0.99109706, 0.94784755, 0.98167344,\n",
              "         0.99025158],\n",
              "        ...,\n",
              "        [0.96393001, 0.98491218, 0.99874134, 0.95843819, 0.99119611,\n",
              "         0.99671249],\n",
              "        [0.96343846, 0.98741176, 0.99864597, 0.95964046, 0.98922515,\n",
              "         0.99720502],\n",
              "        [0.96342501, 0.98737629, 0.9986043 , 0.95974066, 0.98908985,\n",
              "         0.99713528]]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>beta</span></div><div class='xr-var-dims'>(chain, draw, process, measure)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.1597 0.1533 ... -0.2655 -0.213</div><input id='attrs-4d4dd13b-d78e-44be-a70c-10cf78d7d75a' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-4d4dd13b-d78e-44be-a70c-10cf78d7d75a' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-0cf7c559-0623-4f0d-9dde-1a09d97934e6' class='xr-var-data-in' type='checkbox'><label for='data-0cf7c559-0623-4f0d-9dde-1a09d97934e6' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[[[ 0.15966737,  0.15328665,  0.15202392,  0.15971202,\n",
              "           0.15321741,  0.14995951],\n",
              "         [ 0.18115996, -0.05737117, -0.17579616,  0.21885464,\n",
              "          -0.09517925, -0.1754005 ]],\n",
              "\n",
              "        [[ 0.15837451,  0.15347457,  0.15132645,  0.16030434,\n",
              "           0.1517889 ,  0.15056329],\n",
              "         [ 0.18006407, -0.05715795, -0.17510296,  0.21876375,\n",
              "          -0.09682012, -0.17532777]],\n",
              "\n",
              "        [[ 0.15881539,  0.1530026 ,  0.15103259,  0.16032353,\n",
              "           0.1526781 ,  0.15094776],\n",
              "         [ 0.180354  , -0.05612226, -0.1759599 ,  0.21806933,\n",
              "          -0.09518378, -0.17536292]],\n",
              "\n",
              "        ...,\n",
              "\n",
              "        [[ 0.17565416,  0.16661941,  0.16235451,  0.17706535,\n",
              "           0.16417522,  0.16201004],\n",
              "         [ 0.17211276, -0.06852326, -0.18963092,  0.21153081,\n",
              "...\n",
              "          -0.24822927, -0.3824762 ],\n",
              "         [-0.42954366, -0.27256143, -0.19748018, -0.45518469,\n",
              "          -0.24781345, -0.19308574]],\n",
              "\n",
              "        ...,\n",
              "\n",
              "        [[ 0.20364048, -0.18341434, -0.37716638,  0.26739251,\n",
              "          -0.24833231, -0.37810009],\n",
              "         [-0.44914141, -0.29072571, -0.21436139, -0.47469868,\n",
              "          -0.26705259, -0.21096836]],\n",
              "\n",
              "        [[ 0.20733673, -0.18253369, -0.37871358,  0.26851506,\n",
              "          -0.2460635 , -0.37622325],\n",
              "         [-0.45024839, -0.2930652 , -0.21400073, -0.47665224,\n",
              "          -0.26551504, -0.2132768 ]],\n",
              "\n",
              "        [[ 0.20736015, -0.18262942, -0.37848926,  0.26819804,\n",
              "          -0.24609252, -0.37640645],\n",
              "         [-0.44977224, -0.29315793, -0.21412049, -0.47634588,\n",
              "          -0.26545358, -0.21298701]]]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>mu_g</span></div><div class='xr-var-dims'>(chain, draw, group, process)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>-0.2125 1.394 ... -0.3885 0.6707</div><input id='attrs-fd477a96-01a2-4500-b5ed-3a5b79c77a69' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-fd477a96-01a2-4500-b5ed-3a5b79c77a69' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-9f845f15-6462-4171-b10d-d6de7d1ff2cf' class='xr-var-data-in' type='checkbox'><label for='data-9f845f15-6462-4171-b10d-d6de7d1ff2cf' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[[[-0.21245227,  1.39419443],\n",
              "         [ 1.23470702,  0.16561003],\n",
              "         [ 1.41429276,  0.2418334 ],\n",
              "         ...,\n",
              "         [-0.33075007,  1.33711812],\n",
              "         [-0.04192126, -1.05148767],\n",
              "         [-0.04273511, -0.96855075]],\n",
              "\n",
              "        [[-0.21336797,  1.39452965],\n",
              "         [ 1.232694  ,  0.15967368],\n",
              "         [ 1.41580169,  0.23906508],\n",
              "         ...,\n",
              "         [-0.32886376,  1.33848249],\n",
              "         [-0.04336653, -1.05479693],\n",
              "         [-0.04425452, -0.96575917]],\n",
              "\n",
              "        [[-0.21086942,  1.39728473],\n",
              "         [ 1.23345654,  0.15535647],\n",
              "         [ 1.42048808,  0.24076319],\n",
              "         ...,\n",
              "...\n",
              "         ...,\n",
              "         [ 0.93127167,  0.44112395],\n",
              "         [-0.43290804,  0.68162717],\n",
              "         [-0.38813363,  0.67332424]],\n",
              "\n",
              "        [[ 0.94151529,  0.38848565],\n",
              "         [ 0.0337963 , -0.04536186],\n",
              "         [ 0.04656625, -0.1326648 ],\n",
              "         ...,\n",
              "         [ 0.92789656,  0.4418144 ],\n",
              "         [-0.43270387,  0.68214399],\n",
              "         [-0.3886901 ,  0.6708195 ]],\n",
              "\n",
              "        [[ 0.94076218,  0.38841481],\n",
              "         [ 0.03351791, -0.04565443],\n",
              "         [ 0.04694538, -0.13251642],\n",
              "         ...,\n",
              "         [ 0.92801007,  0.44199319],\n",
              "         [-0.43318379,  0.68232241],\n",
              "         [-0.38854783,  0.67069118]]]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>x</span></div><div class='xr-var-dims'>(chain, draw, subject, process)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.05988 -0.9823 ... 0.5166 1.192</div><input id='attrs-305bc0e8-56fd-4d69-82f5-db7de34c60de' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-305bc0e8-56fd-4d69-82f5-db7de34c60de' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-dae452ef-6856-4b77-812d-a9510c2151fa' class='xr-var-data-in' type='checkbox'><label for='data-dae452ef-6856-4b77-812d-a9510c2151fa' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[[[ 0.05988473, -0.98231393],\n",
              "         [ 0.06335564, -0.97971414],\n",
              "         [ 0.06899993, -0.98886001],\n",
              "         ...,\n",
              "         [-1.69442237,  0.20367787],\n",
              "         [-1.69333059,  0.21889305],\n",
              "         [-1.70297033,  0.18187137]],\n",
              "\n",
              "        [[ 0.05700426, -0.97382159],\n",
              "         [ 0.07129534, -0.9784868 ],\n",
              "         [ 0.06343137, -0.97679785],\n",
              "         ...,\n",
              "         [-1.67972062,  0.20450131],\n",
              "         [-1.69761696,  0.20524085],\n",
              "         [-1.67407469,  0.20189554]],\n",
              "\n",
              "        [[ 0.06834035, -0.96696917],\n",
              "         [ 0.05702963, -0.97389528],\n",
              "         [ 0.07546938, -0.97585785],\n",
              "         ...,\n",
              "...\n",
              "         ...,\n",
              "         [ 0.52115851,  1.19628519],\n",
              "         [ 0.5166023 ,  1.19425235],\n",
              "         [ 0.52311882,  1.1966767 ]],\n",
              "\n",
              "        [[-0.40531425,  0.620776  ],\n",
              "         [-0.40289609,  0.62116134],\n",
              "         [-0.40246163,  0.624884  ],\n",
              "         ...,\n",
              "         [ 0.52279481,  1.19360306],\n",
              "         [ 0.52309536,  1.19710843],\n",
              "         [ 0.51758907,  1.19146137]],\n",
              "\n",
              "        [[-0.4052075 ,  0.62088084],\n",
              "         [-0.40345903,  0.6214447 ],\n",
              "         [-0.40251669,  0.62541381],\n",
              "         ...,\n",
              "         [ 0.52315285,  1.19401246],\n",
              "         [ 0.52254502,  1.19751602],\n",
              "         [ 0.51664235,  1.19223006]]]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>sigma_p</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.009367 0.009306 ... 0.003305</div><input id='attrs-b4d3834f-3f94-4366-b4b5-65b9c20614c0' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-b4d3834f-3f94-4366-b4b5-65b9c20614c0' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-4d9a6d81-2c44-4a19-9d88-acb0c37287fa' class='xr-var-data-in' type='checkbox'><label for='data-4d9a6d81-2c44-4a19-9d88-acb0c37287fa' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[0.00936713, 0.00930583, 0.00938394, ..., 0.00876134, 0.00839052,\n",
              "        0.00801617],\n",
              "       [0.00557032, 0.00579348, 0.00554972, ..., 0.00306899, 0.00332108,\n",
              "        0.00330534]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>sigma_y</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.01012 0.00993 ... 0.0101 0.01011</div><input id='attrs-89d7a46c-2bd7-471e-90cb-ac42848f1427' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-89d7a46c-2bd7-471e-90cb-ac42848f1427' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-9ae73068-ac37-4699-b69f-1547758f8ec7' class='xr-var-data-in' type='checkbox'><label for='data-9ae73068-ac37-4699-b69f-1547758f8ec7' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[0.01012303, 0.00992994, 0.01001293, ..., 0.00992188, 0.00986725,\n",
              "        0.01012489],\n",
              "       [0.00989491, 0.01001952, 0.01006367, ..., 0.01023704, 0.01010467,\n",
              "        0.01011168]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>mu_y</span></div><div class='xr-var-dims'>(chain, draw, subject, measure)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.5966 0.8792 ... 0.5455 0.5487</div><input id='attrs-302397fe-68ef-4bfc-bcf8-e5fcb387eccb' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-302397fe-68ef-4bfc-bcf8-e5fcb387eccb' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-5c28167a-adfb-4043-a2a2-d919a73a8c89' class='xr-var-data-in' type='checkbox'><label for='data-5c28167a-adfb-4043-a2a2-d919a73a8c89' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[[[0.5966381 , 0.87922889, 1.01945835, 0.55083531, 0.92339331,\n",
              "          1.0182794 ],\n",
              "         [0.59766327, 0.87961178, 1.01952897, 0.55195864, 0.92367766,\n",
              "          1.01834389],\n",
              "         [0.59690762, 0.88100169, 1.02199485, 0.55085848, 0.92541296,\n",
              "          1.02079449],\n",
              "         ...,\n",
              "         [0.53138674, 0.54227531, 0.5442689 , 0.5302112 , 0.54172109,\n",
              "          0.54718082],\n",
              "         [0.53431744, 0.54156975, 0.54176011, 0.53371549, 0.54044021,\n",
              "          0.54467579],\n",
              "         [0.52607145, 0.54221608, 0.54680291, 0.52407354, 0.54248693,\n",
              "          0.54972384]],\n",
              "\n",
              "        [[0.59704229, 0.87732856, 1.01599379, 0.55228535, 0.92396093,\n",
              "          1.01760279],\n",
              "         [0.5984656 , 0.87978853, 1.0189733 , 0.5535557 , 0.92658184,\n",
              "          1.02057244],\n",
              "         [0.59752427, 0.87848507, 1.01748753, 0.55266455, 0.92522465,\n",
              "          1.0190923 ],\n",
              "...\n",
              "         [0.53441518, 0.54218057, 0.54522455, 0.53108517, 0.54366486,\n",
              "          0.54594961],\n",
              "         [0.5328992 , 0.54109841, 0.54436057, 0.52949503, 0.54266017,\n",
              "          0.54508893],\n",
              "         [0.53430013, 0.54375845, 0.54765435, 0.53070819, 0.54551445,\n",
              "          0.54836491]],\n",
              "\n",
              "        [[0.60014615, 0.87936295, 1.01902768, 0.55531077, 0.92399335,\n",
              "          1.01741844],\n",
              "         [0.60025511, 0.87887833, 1.01824517, 0.55551112, 0.92341338,\n",
              "          1.01664021],\n",
              "         [0.59866531, 0.87754266, 1.01703863, 0.55387318, 0.92212787,\n",
              "          1.01544014],\n",
              "         ...,\n",
              "         [0.5348724 , 0.54179896, 0.54493403, 0.53128632, 0.54339097,\n",
              "          0.54590803],\n",
              "         [0.53317056, 0.54088287, 0.5444139 , 0.52945439, 0.54261051,\n",
              "          0.5453906 ],\n",
              "         [0.53432406, 0.54351049, 0.54777984, 0.53038925, 0.5454663 ,\n",
              "          0.54873825]]]])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-92b0ed93-0da1-40ad-8900-3776972034f0' class='xr-section-summary-in' type='checkbox'  checked><label for='section-92b0ed93-0da1-40ad-8900-3776972034f0' class='xr-section-summary' >Attributes: <span>(6)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>created_at :</span></dt><dd>2022-10-05T04:33:10.841898</dd><dt><span>arviz_version :</span></dt><dd>0.12.1</dd><dt><span>inference_library :</span></dt><dd>pymc</dd><dt><span>inference_library_version :</span></dt><dd>4.1.4</dd><dt><span>sampling_time :</span></dt><dd>122.29010105133057</dd><dt><span>tuning_steps :</span></dt><dd>1000</dd></dl></div></li></ul></div></div><br></div>\n",
              "                      </ul>\n",
              "                  </div>\n",
              "            </li>\n",
              "            \n",
              "            <li class = \"xr-section-item\">\n",
              "                  <input id=\"idata_log_likelihood2298cca6-e1dc-4c17-b46f-80e947417da8\" class=\"xr-section-summary-in\" type=\"checkbox\">\n",
              "                  <label for=\"idata_log_likelihood2298cca6-e1dc-4c17-b46f-80e947417da8\" class = \"xr-section-summary\">log_likelihood</label>\n",
              "                  <div class=\"xr-section-inline-details\"></div>\n",
              "                  <div class=\"xr-section-details\">\n",
              "                      <ul id=\"xr-dataset-coord-list\" class=\"xr-var-list\">\n",
              "                          <div style=\"padding-left:2rem;\"><div><svg style=\"position: absolute; width: 0; height: 0; overflow: hidden\">\n",
              "<defs>\n",
              "<symbol id=\"icon-database\" viewBox=\"0 0 32 32\">\n",
              "<path d=\"M16 0c-8.837 0-16 2.239-16 5v4c0 2.761 7.163 5 16 5s16-2.239 16-5v-4c0-2.761-7.163-5-16-5z\"></path>\n",
              "<path d=\"M16 17c-8.837 0-16-2.239-16-5v6c0 2.761 7.163 5 16 5s16-2.239 16-5v-6c0 2.761-7.163 5-16 5z\"></path>\n",
              "<path d=\"M16 26c-8.837 0-16-2.239-16-5v6c0 2.761 7.163 5 16 5s16-2.239 16-5v-6c0 2.761-7.163 5-16 5z\"></path>\n",
              "</symbol>\n",
              "<symbol id=\"icon-file-text2\" viewBox=\"0 0 32 32\">\n",
              "<path d=\"M28.681 7.159c-0.694-0.947-1.662-2.053-2.724-3.116s-2.169-2.030-3.116-2.724c-1.612-1.182-2.393-1.319-2.841-1.319h-15.5c-1.378 0-2.5 1.121-2.5 2.5v27c0 1.378 1.122 2.5 2.5 2.5h23c1.378 0 2.5-1.122 2.5-2.5v-19.5c0-0.448-0.137-1.23-1.319-2.841zM24.543 5.457c0.959 0.959 1.712 1.825 2.268 2.543h-4.811v-4.811c0.718 0.556 1.584 1.309 2.543 2.268zM28 29.5c0 0.271-0.229 0.5-0.5 0.5h-23c-0.271 0-0.5-0.229-0.5-0.5v-27c0-0.271 0.229-0.5 0.5-0.5 0 0 15.499-0 15.5 0v7c0 0.552 0.448 1 1 1h7v19.5z\"></path>\n",
              "<path d=\"M23 26h-14c-0.552 0-1-0.448-1-1s0.448-1 1-1h14c0.552 0 1 0.448 1 1s-0.448 1-1 1z\"></path>\n",
              "<path d=\"M23 22h-14c-0.552 0-1-0.448-1-1s0.448-1 1-1h14c0.552 0 1 0.448 1 1s-0.448 1-1 1z\"></path>\n",
              "<path d=\"M23 18h-14c-0.552 0-1-0.448-1-1s0.448-1 1-1h14c0.552 0 1 0.448 1 1s-0.448 1-1 1z\"></path>\n",
              "</symbol>\n",
              "</defs>\n",
              "</svg>\n",
              "<style>/* CSS stylesheet for displaying xarray objects in jupyterlab.\n",
              " *\n",
              " */\n",
              "\n",
              ":root {\n",
              "  --xr-font-color0: var(--jp-content-font-color0, rgba(0, 0, 0, 1));\n",
              "  --xr-font-color2: var(--jp-content-font-color2, rgba(0, 0, 0, 0.54));\n",
              "  --xr-font-color3: var(--jp-content-font-color3, rgba(0, 0, 0, 0.38));\n",
              "  --xr-border-color: var(--jp-border-color2, #e0e0e0);\n",
              "  --xr-disabled-color: var(--jp-layout-color3, #bdbdbd);\n",
              "  --xr-background-color: var(--jp-layout-color0, white);\n",
              "  --xr-background-color-row-even: var(--jp-layout-color1, white);\n",
              "  --xr-background-color-row-odd: var(--jp-layout-color2, #eeeeee);\n",
              "}\n",
              "\n",
              "html[theme=dark],\n",
              "body.vscode-dark {\n",
              "  --xr-font-color0: rgba(255, 255, 255, 1);\n",
              "  --xr-font-color2: rgba(255, 255, 255, 0.54);\n",
              "  --xr-font-color3: rgba(255, 255, 255, 0.38);\n",
              "  --xr-border-color: #1F1F1F;\n",
              "  --xr-disabled-color: #515151;\n",
              "  --xr-background-color: #111111;\n",
              "  --xr-background-color-row-even: #111111;\n",
              "  --xr-background-color-row-odd: #313131;\n",
              "}\n",
              "\n",
              ".xr-wrap {\n",
              "  display: block !important;\n",
              "  min-width: 300px;\n",
              "  max-width: 700px;\n",
              "}\n",
              "\n",
              ".xr-text-repr-fallback {\n",
              "  /* fallback to plain text repr when CSS is not injected (untrusted notebook) */\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-header {\n",
              "  padding-top: 6px;\n",
              "  padding-bottom: 6px;\n",
              "  margin-bottom: 4px;\n",
              "  border-bottom: solid 1px var(--xr-border-color);\n",
              "}\n",
              "\n",
              ".xr-header > div,\n",
              ".xr-header > ul {\n",
              "  display: inline;\n",
              "  margin-top: 0;\n",
              "  margin-bottom: 0;\n",
              "}\n",
              "\n",
              ".xr-obj-type,\n",
              ".xr-array-name {\n",
              "  margin-left: 2px;\n",
              "  margin-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-obj-type {\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-sections {\n",
              "  padding-left: 0 !important;\n",
              "  display: grid;\n",
              "  grid-template-columns: 150px auto auto 1fr 20px 20px;\n",
              "}\n",
              "\n",
              ".xr-section-item {\n",
              "  display: contents;\n",
              "}\n",
              "\n",
              ".xr-section-item input {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-section-item input + label {\n",
              "  color: var(--xr-disabled-color);\n",
              "}\n",
              "\n",
              ".xr-section-item input:enabled + label {\n",
              "  cursor: pointer;\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-section-item input:enabled + label:hover {\n",
              "  color: var(--xr-font-color0);\n",
              "}\n",
              "\n",
              ".xr-section-summary {\n",
              "  grid-column: 1;\n",
              "  color: var(--xr-font-color2);\n",
              "  font-weight: 500;\n",
              "}\n",
              "\n",
              ".xr-section-summary > span {\n",
              "  display: inline-block;\n",
              "  padding-left: 0.5em;\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:disabled + label {\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-section-summary-in + label:before {\n",
              "  display: inline-block;\n",
              "  content: '►';\n",
              "  font-size: 11px;\n",
              "  width: 15px;\n",
              "  text-align: center;\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:disabled + label:before {\n",
              "  color: var(--xr-disabled-color);\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:checked + label:before {\n",
              "  content: '▼';\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:checked + label > span {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-section-summary,\n",
              ".xr-section-inline-details {\n",
              "  padding-top: 4px;\n",
              "  padding-bottom: 4px;\n",
              "}\n",
              "\n",
              ".xr-section-inline-details {\n",
              "  grid-column: 2 / -1;\n",
              "}\n",
              "\n",
              ".xr-section-details {\n",
              "  display: none;\n",
              "  grid-column: 1 / -1;\n",
              "  margin-bottom: 5px;\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:checked ~ .xr-section-details {\n",
              "  display: contents;\n",
              "}\n",
              "\n",
              ".xr-array-wrap {\n",
              "  grid-column: 1 / -1;\n",
              "  display: grid;\n",
              "  grid-template-columns: 20px auto;\n",
              "}\n",
              "\n",
              ".xr-array-wrap > label {\n",
              "  grid-column: 1;\n",
              "  vertical-align: top;\n",
              "}\n",
              "\n",
              ".xr-preview {\n",
              "  color: var(--xr-font-color3);\n",
              "}\n",
              "\n",
              ".xr-array-preview,\n",
              ".xr-array-data {\n",
              "  padding: 0 5px !important;\n",
              "  grid-column: 2;\n",
              "}\n",
              "\n",
              ".xr-array-data,\n",
              ".xr-array-in:checked ~ .xr-array-preview {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-array-in:checked ~ .xr-array-data,\n",
              ".xr-array-preview {\n",
              "  display: inline-block;\n",
              "}\n",
              "\n",
              ".xr-dim-list {\n",
              "  display: inline-block !important;\n",
              "  list-style: none;\n",
              "  padding: 0 !important;\n",
              "  margin: 0;\n",
              "}\n",
              "\n",
              ".xr-dim-list li {\n",
              "  display: inline-block;\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "}\n",
              "\n",
              ".xr-dim-list:before {\n",
              "  content: '(';\n",
              "}\n",
              "\n",
              ".xr-dim-list:after {\n",
              "  content: ')';\n",
              "}\n",
              "\n",
              ".xr-dim-list li:not(:last-child):after {\n",
              "  content: ',';\n",
              "  padding-right: 5px;\n",
              "}\n",
              "\n",
              ".xr-has-index {\n",
              "  font-weight: bold;\n",
              "}\n",
              "\n",
              ".xr-var-list,\n",
              ".xr-var-item {\n",
              "  display: contents;\n",
              "}\n",
              "\n",
              ".xr-var-item > div,\n",
              ".xr-var-item label,\n",
              ".xr-var-item > .xr-var-name span {\n",
              "  background-color: var(--xr-background-color-row-even);\n",
              "  margin-bottom: 0;\n",
              "}\n",
              "\n",
              ".xr-var-item > .xr-var-name:hover span {\n",
              "  padding-right: 5px;\n",
              "}\n",
              "\n",
              ".xr-var-list > li:nth-child(odd) > div,\n",
              ".xr-var-list > li:nth-child(odd) > label,\n",
              ".xr-var-list > li:nth-child(odd) > .xr-var-name span {\n",
              "  background-color: var(--xr-background-color-row-odd);\n",
              "}\n",
              "\n",
              ".xr-var-name {\n",
              "  grid-column: 1;\n",
              "}\n",
              "\n",
              ".xr-var-dims {\n",
              "  grid-column: 2;\n",
              "}\n",
              "\n",
              ".xr-var-dtype {\n",
              "  grid-column: 3;\n",
              "  text-align: right;\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-var-preview {\n",
              "  grid-column: 4;\n",
              "}\n",
              "\n",
              ".xr-var-name,\n",
              ".xr-var-dims,\n",
              ".xr-var-dtype,\n",
              ".xr-preview,\n",
              ".xr-attrs dt {\n",
              "  white-space: nowrap;\n",
              "  overflow: hidden;\n",
              "  text-overflow: ellipsis;\n",
              "  padding-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-var-name:hover,\n",
              ".xr-var-dims:hover,\n",
              ".xr-var-dtype:hover,\n",
              ".xr-attrs dt:hover {\n",
              "  overflow: visible;\n",
              "  width: auto;\n",
              "  z-index: 1;\n",
              "}\n",
              "\n",
              ".xr-var-attrs,\n",
              ".xr-var-data {\n",
              "  display: none;\n",
              "  background-color: var(--xr-background-color) !important;\n",
              "  padding-bottom: 5px !important;\n",
              "}\n",
              "\n",
              ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
              ".xr-var-data-in:checked ~ .xr-var-data {\n",
              "  display: block;\n",
              "}\n",
              "\n",
              ".xr-var-data > table {\n",
              "  float: right;\n",
              "}\n",
              "\n",
              ".xr-var-name span,\n",
              ".xr-var-data,\n",
              ".xr-attrs {\n",
              "  padding-left: 25px !important;\n",
              "}\n",
              "\n",
              ".xr-attrs,\n",
              ".xr-var-attrs,\n",
              ".xr-var-data {\n",
              "  grid-column: 1 / -1;\n",
              "}\n",
              "\n",
              "dl.xr-attrs {\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "  display: grid;\n",
              "  grid-template-columns: 125px auto;\n",
              "}\n",
              "\n",
              ".xr-attrs dt,\n",
              ".xr-attrs dd {\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "  float: left;\n",
              "  padding-right: 10px;\n",
              "  width: auto;\n",
              "}\n",
              "\n",
              ".xr-attrs dt {\n",
              "  font-weight: normal;\n",
              "  grid-column: 1;\n",
              "}\n",
              "\n",
              ".xr-attrs dt:hover span {\n",
              "  display: inline-block;\n",
              "  background: var(--xr-background-color);\n",
              "  padding-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-attrs dd {\n",
              "  grid-column: 2;\n",
              "  white-space: pre-wrap;\n",
              "  word-break: break-all;\n",
              "}\n",
              "\n",
              ".xr-icon-database,\n",
              ".xr-icon-file-text2 {\n",
              "  display: inline-block;\n",
              "  vertical-align: middle;\n",
              "  width: 1em;\n",
              "  height: 1.5em !important;\n",
              "  stroke-width: 0;\n",
              "  stroke: currentColor;\n",
              "  fill: currentColor;\n",
              "}\n",
              "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n",
              "Dimensions:  (chain: 2, draw: 1000, subject: 420, measure: 6)\n",
              "Coordinates:\n",
              "  * chain    (chain) int64 0 1\n",
              "  * draw     (draw) int64 0 1 2 3 4 5 6 7 8 ... 992 993 994 995 996 997 998 999\n",
              "  * subject  (subject) int64 0 1 2 3 4 5 6 7 ... 412 413 414 415 416 417 418 419\n",
              "  * measure  (measure) &lt;U2 &#x27;lr&#x27; &#x27;la&#x27; &#x27;af&#x27; &#x27;pr&#x27; &#x27;gn&#x27; &#x27;fb&#x27;\n",
              "Data variables:\n",
              "    obs_y    (chain, draw, subject, measure) float64 3.263 2.947 ... 3.45 3.63\n",
              "Attributes:\n",
              "    created_at:                 2022-10-05T04:33:13.057236\n",
              "    arviz_version:              0.12.1\n",
              "    inference_library:          pymc\n",
              "    inference_library_version:  4.1.4</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-5a97a900-fa62-4050-91a3-9a1a5edf9be0' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-5a97a900-fa62-4050-91a3-9a1a5edf9be0' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>chain</span>: 2</li><li><span class='xr-has-index'>draw</span>: 1000</li><li><span class='xr-has-index'>subject</span>: 420</li><li><span class='xr-has-index'>measure</span>: 6</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-b8b4d082-71a0-43aa-9a9e-b2b50e669dc8' class='xr-section-summary-in' type='checkbox'  checked><label for='section-b8b4d082-71a0-43aa-9a9e-b2b50e669dc8' class='xr-section-summary' >Coordinates: <span>(4)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>chain</span></div><div class='xr-var-dims'>(chain)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1</div><input id='attrs-4d9045b7-b639-44a1-8b10-f1511a878b01' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-4d9045b7-b639-44a1-8b10-f1511a878b01' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-e934b4df-0619-4f46-979b-84c29f86ab58' class='xr-var-data-in' type='checkbox'><label for='data-e934b4df-0619-4f46-979b-84c29f86ab58' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0, 1])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>draw</span></div><div class='xr-var-dims'>(draw)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 5 ... 995 996 997 998 999</div><input id='attrs-5141fa11-ad84-43fb-9d51-2fef60cbe692' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-5141fa11-ad84-43fb-9d51-2fef60cbe692' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-43954fea-babf-4801-af47-dc2680b023b2' class='xr-var-data-in' type='checkbox'><label for='data-43954fea-babf-4801-af47-dc2680b023b2' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([  0,   1,   2, ..., 997, 998, 999])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>subject</span></div><div class='xr-var-dims'>(subject)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 5 ... 415 416 417 418 419</div><input id='attrs-ac52049f-6fff-4d5b-a790-74ff5aabb6fb' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-ac52049f-6fff-4d5b-a790-74ff5aabb6fb' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-f7754b71-bbdb-4303-a211-672fee89e1de' class='xr-var-data-in' type='checkbox'><label for='data-f7754b71-bbdb-4303-a211-672fee89e1de' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([  0,   1,   2, ..., 417, 418, 419])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>measure</span></div><div class='xr-var-dims'>(measure)</div><div class='xr-var-dtype'>&lt;U2</div><div class='xr-var-preview xr-preview'>&#x27;lr&#x27; &#x27;la&#x27; &#x27;af&#x27; &#x27;pr&#x27; &#x27;gn&#x27; &#x27;fb&#x27;</div><input id='attrs-1d4af9e7-9be3-45b4-9acf-1d386cd7f96e' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-1d4af9e7-9be3-45b4-9acf-1d386cd7f96e' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-02a46e39-614b-4272-aefe-23bc311b52f2' class='xr-var-data-in' type='checkbox'><label for='data-02a46e39-614b-4272-aefe-23bc311b52f2' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([&#x27;lr&#x27;, &#x27;la&#x27;, &#x27;af&#x27;, &#x27;pr&#x27;, &#x27;gn&#x27;, &#x27;fb&#x27;], dtype=&#x27;&lt;U2&#x27;)</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-9ee5457a-e3dd-40ff-9e88-7f35118b6c47' class='xr-section-summary-in' type='checkbox'  checked><label for='section-9ee5457a-e3dd-40ff-9e88-7f35118b6c47' class='xr-section-summary' >Data variables: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>obs_y</span></div><div class='xr-var-dims'>(chain, draw, subject, measure)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>3.263 2.947 1.514 ... 3.45 3.63</div><input id='attrs-ca50aaa6-80f4-4b48-b8a2-81deb810e032' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-ca50aaa6-80f4-4b48-b8a2-81deb810e032' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-6079e92d-a083-426b-a0b0-b740e1c04918' class='xr-var-data-in' type='checkbox'><label for='data-6079e92d-a083-426b-a0b0-b740e1c04918' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[[[ 3.2627566 ,  2.94665756,  1.51405069,  3.58263918,\n",
              "           2.65197353,  3.55543132],\n",
              "         [ 2.81846901,  3.63899187,  3.46538231,  3.67007873,\n",
              "           3.59721624,  3.56840448],\n",
              "         [ 2.94426405,  2.91046175,  3.60244983,  2.46132479,\n",
              "           2.64077867,  3.46734706],\n",
              "         ...,\n",
              "         [ 3.65099601,  2.71412012,  2.73475494,  3.34097902,\n",
              "           2.91968354,  3.39697536],\n",
              "         [ 3.12911209,  2.25056662,  3.25766791,  2.88800983,\n",
              "           3.65484636, -0.04538886],\n",
              "         [ 2.89592304,  3.6725895 ,  3.67358352,  3.64813272,\n",
              "           3.60319101,  3.65327477]],\n",
              "\n",
              "        [[ 3.22740465,  2.683736  ,  2.12689345,  3.6512842 ,\n",
              "           2.54614864,  3.60153954],\n",
              "         [ 2.90861395,  3.65191594,  3.43803329,  3.690777  ,\n",
              "           3.45384863,  3.66347719],\n",
              "         [ 2.85645707,  3.18689723,  3.34082841,  2.70518373,\n",
              "           2.64707434,  3.35144979],\n",
              "...\n",
              "         [ 3.54340781,  2.7254136 ,  2.59882474,  3.40855836,\n",
              "           2.66355133,  3.48121983],\n",
              "         [ 3.26588217,  2.32496367,  3.46011652,  3.32436716,\n",
              "           3.67554048, -0.16965197],\n",
              "         [ 3.5810394 ,  3.67088286,  3.67429439,  3.58392247,\n",
              "           3.44690359,  3.61853883]],\n",
              "\n",
              "        [[ 2.88778544,  2.96206657,  1.59803755,  3.67501771,\n",
              "           2.56410301,  3.59417145],\n",
              "         [ 3.1204831 ,  3.65661972,  3.37587269,  3.64063924,\n",
              "           3.60807743,  3.47757803],\n",
              "         [ 2.71840303,  3.27456215,  3.29765949,  2.88011131,\n",
              "           3.05435184,  2.98699955],\n",
              "         ...,\n",
              "         [ 3.51862206,  2.77732133,  2.64134844,  3.4225708 ,\n",
              "           2.70240809,  3.48335135],\n",
              "         [ 3.24111461,  2.36092854,  3.46316972,  3.32751955,\n",
              "           3.67495077, -0.24813937],\n",
              "         [ 3.58150375,  3.67232997,  3.67284087,  3.59637153,\n",
              "           3.44973593,  3.62973097]]]])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-0228b089-7b47-411d-a2ea-71f25f430537' class='xr-section-summary-in' type='checkbox'  checked><label for='section-0228b089-7b47-411d-a2ea-71f25f430537' class='xr-section-summary' >Attributes: <span>(4)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>created_at :</span></dt><dd>2022-10-05T04:33:13.057236</dd><dt><span>arviz_version :</span></dt><dd>0.12.1</dd><dt><span>inference_library :</span></dt><dd>pymc</dd><dt><span>inference_library_version :</span></dt><dd>4.1.4</dd></dl></div></li></ul></div></div><br></div>\n",
              "                      </ul>\n",
              "                  </div>\n",
              "            </li>\n",
              "            \n",
              "            <li class = \"xr-section-item\">\n",
              "                  <input id=\"idata_sample_statsd3cd73e9-bb6b-487c-b85a-7984ed6da9b6\" class=\"xr-section-summary-in\" type=\"checkbox\">\n",
              "                  <label for=\"idata_sample_statsd3cd73e9-bb6b-487c-b85a-7984ed6da9b6\" class = \"xr-section-summary\">sample_stats</label>\n",
              "                  <div class=\"xr-section-inline-details\"></div>\n",
              "                  <div class=\"xr-section-details\">\n",
              "                      <ul id=\"xr-dataset-coord-list\" class=\"xr-var-list\">\n",
              "                          <div style=\"padding-left:2rem;\"><div><svg style=\"position: absolute; width: 0; height: 0; overflow: hidden\">\n",
              "<defs>\n",
              "<symbol id=\"icon-database\" viewBox=\"0 0 32 32\">\n",
              "<path d=\"M16 0c-8.837 0-16 2.239-16 5v4c0 2.761 7.163 5 16 5s16-2.239 16-5v-4c0-2.761-7.163-5-16-5z\"></path>\n",
              "<path d=\"M16 17c-8.837 0-16-2.239-16-5v6c0 2.761 7.163 5 16 5s16-2.239 16-5v-6c0 2.761-7.163 5-16 5z\"></path>\n",
              "<path d=\"M16 26c-8.837 0-16-2.239-16-5v6c0 2.761 7.163 5 16 5s16-2.239 16-5v-6c0 2.761-7.163 5-16 5z\"></path>\n",
              "</symbol>\n",
              "<symbol id=\"icon-file-text2\" viewBox=\"0 0 32 32\">\n",
              "<path d=\"M28.681 7.159c-0.694-0.947-1.662-2.053-2.724-3.116s-2.169-2.030-3.116-2.724c-1.612-1.182-2.393-1.319-2.841-1.319h-15.5c-1.378 0-2.5 1.121-2.5 2.5v27c0 1.378 1.122 2.5 2.5 2.5h23c1.378 0 2.5-1.122 2.5-2.5v-19.5c0-0.448-0.137-1.23-1.319-2.841zM24.543 5.457c0.959 0.959 1.712 1.825 2.268 2.543h-4.811v-4.811c0.718 0.556 1.584 1.309 2.543 2.268zM28 29.5c0 0.271-0.229 0.5-0.5 0.5h-23c-0.271 0-0.5-0.229-0.5-0.5v-27c0-0.271 0.229-0.5 0.5-0.5 0 0 15.499-0 15.5 0v7c0 0.552 0.448 1 1 1h7v19.5z\"></path>\n",
              "<path d=\"M23 26h-14c-0.552 0-1-0.448-1-1s0.448-1 1-1h14c0.552 0 1 0.448 1 1s-0.448 1-1 1z\"></path>\n",
              "<path d=\"M23 22h-14c-0.552 0-1-0.448-1-1s0.448-1 1-1h14c0.552 0 1 0.448 1 1s-0.448 1-1 1z\"></path>\n",
              "<path d=\"M23 18h-14c-0.552 0-1-0.448-1-1s0.448-1 1-1h14c0.552 0 1 0.448 1 1s-0.448 1-1 1z\"></path>\n",
              "</symbol>\n",
              "</defs>\n",
              "</svg>\n",
              "<style>/* CSS stylesheet for displaying xarray objects in jupyterlab.\n",
              " *\n",
              " */\n",
              "\n",
              ":root {\n",
              "  --xr-font-color0: var(--jp-content-font-color0, rgba(0, 0, 0, 1));\n",
              "  --xr-font-color2: var(--jp-content-font-color2, rgba(0, 0, 0, 0.54));\n",
              "  --xr-font-color3: var(--jp-content-font-color3, rgba(0, 0, 0, 0.38));\n",
              "  --xr-border-color: var(--jp-border-color2, #e0e0e0);\n",
              "  --xr-disabled-color: var(--jp-layout-color3, #bdbdbd);\n",
              "  --xr-background-color: var(--jp-layout-color0, white);\n",
              "  --xr-background-color-row-even: var(--jp-layout-color1, white);\n",
              "  --xr-background-color-row-odd: var(--jp-layout-color2, #eeeeee);\n",
              "}\n",
              "\n",
              "html[theme=dark],\n",
              "body.vscode-dark {\n",
              "  --xr-font-color0: rgba(255, 255, 255, 1);\n",
              "  --xr-font-color2: rgba(255, 255, 255, 0.54);\n",
              "  --xr-font-color3: rgba(255, 255, 255, 0.38);\n",
              "  --xr-border-color: #1F1F1F;\n",
              "  --xr-disabled-color: #515151;\n",
              "  --xr-background-color: #111111;\n",
              "  --xr-background-color-row-even: #111111;\n",
              "  --xr-background-color-row-odd: #313131;\n",
              "}\n",
              "\n",
              ".xr-wrap {\n",
              "  display: block !important;\n",
              "  min-width: 300px;\n",
              "  max-width: 700px;\n",
              "}\n",
              "\n",
              ".xr-text-repr-fallback {\n",
              "  /* fallback to plain text repr when CSS is not injected (untrusted notebook) */\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-header {\n",
              "  padding-top: 6px;\n",
              "  padding-bottom: 6px;\n",
              "  margin-bottom: 4px;\n",
              "  border-bottom: solid 1px var(--xr-border-color);\n",
              "}\n",
              "\n",
              ".xr-header > div,\n",
              ".xr-header > ul {\n",
              "  display: inline;\n",
              "  margin-top: 0;\n",
              "  margin-bottom: 0;\n",
              "}\n",
              "\n",
              ".xr-obj-type,\n",
              ".xr-array-name {\n",
              "  margin-left: 2px;\n",
              "  margin-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-obj-type {\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-sections {\n",
              "  padding-left: 0 !important;\n",
              "  display: grid;\n",
              "  grid-template-columns: 150px auto auto 1fr 20px 20px;\n",
              "}\n",
              "\n",
              ".xr-section-item {\n",
              "  display: contents;\n",
              "}\n",
              "\n",
              ".xr-section-item input {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-section-item input + label {\n",
              "  color: var(--xr-disabled-color);\n",
              "}\n",
              "\n",
              ".xr-section-item input:enabled + label {\n",
              "  cursor: pointer;\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-section-item input:enabled + label:hover {\n",
              "  color: var(--xr-font-color0);\n",
              "}\n",
              "\n",
              ".xr-section-summary {\n",
              "  grid-column: 1;\n",
              "  color: var(--xr-font-color2);\n",
              "  font-weight: 500;\n",
              "}\n",
              "\n",
              ".xr-section-summary > span {\n",
              "  display: inline-block;\n",
              "  padding-left: 0.5em;\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:disabled + label {\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-section-summary-in + label:before {\n",
              "  display: inline-block;\n",
              "  content: '►';\n",
              "  font-size: 11px;\n",
              "  width: 15px;\n",
              "  text-align: center;\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:disabled + label:before {\n",
              "  color: var(--xr-disabled-color);\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:checked + label:before {\n",
              "  content: '▼';\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:checked + label > span {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-section-summary,\n",
              ".xr-section-inline-details {\n",
              "  padding-top: 4px;\n",
              "  padding-bottom: 4px;\n",
              "}\n",
              "\n",
              ".xr-section-inline-details {\n",
              "  grid-column: 2 / -1;\n",
              "}\n",
              "\n",
              ".xr-section-details {\n",
              "  display: none;\n",
              "  grid-column: 1 / -1;\n",
              "  margin-bottom: 5px;\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:checked ~ .xr-section-details {\n",
              "  display: contents;\n",
              "}\n",
              "\n",
              ".xr-array-wrap {\n",
              "  grid-column: 1 / -1;\n",
              "  display: grid;\n",
              "  grid-template-columns: 20px auto;\n",
              "}\n",
              "\n",
              ".xr-array-wrap > label {\n",
              "  grid-column: 1;\n",
              "  vertical-align: top;\n",
              "}\n",
              "\n",
              ".xr-preview {\n",
              "  color: var(--xr-font-color3);\n",
              "}\n",
              "\n",
              ".xr-array-preview,\n",
              ".xr-array-data {\n",
              "  padding: 0 5px !important;\n",
              "  grid-column: 2;\n",
              "}\n",
              "\n",
              ".xr-array-data,\n",
              ".xr-array-in:checked ~ .xr-array-preview {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-array-in:checked ~ .xr-array-data,\n",
              ".xr-array-preview {\n",
              "  display: inline-block;\n",
              "}\n",
              "\n",
              ".xr-dim-list {\n",
              "  display: inline-block !important;\n",
              "  list-style: none;\n",
              "  padding: 0 !important;\n",
              "  margin: 0;\n",
              "}\n",
              "\n",
              ".xr-dim-list li {\n",
              "  display: inline-block;\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "}\n",
              "\n",
              ".xr-dim-list:before {\n",
              "  content: '(';\n",
              "}\n",
              "\n",
              ".xr-dim-list:after {\n",
              "  content: ')';\n",
              "}\n",
              "\n",
              ".xr-dim-list li:not(:last-child):after {\n",
              "  content: ',';\n",
              "  padding-right: 5px;\n",
              "}\n",
              "\n",
              ".xr-has-index {\n",
              "  font-weight: bold;\n",
              "}\n",
              "\n",
              ".xr-var-list,\n",
              ".xr-var-item {\n",
              "  display: contents;\n",
              "}\n",
              "\n",
              ".xr-var-item > div,\n",
              ".xr-var-item label,\n",
              ".xr-var-item > .xr-var-name span {\n",
              "  background-color: var(--xr-background-color-row-even);\n",
              "  margin-bottom: 0;\n",
              "}\n",
              "\n",
              ".xr-var-item > .xr-var-name:hover span {\n",
              "  padding-right: 5px;\n",
              "}\n",
              "\n",
              ".xr-var-list > li:nth-child(odd) > div,\n",
              ".xr-var-list > li:nth-child(odd) > label,\n",
              ".xr-var-list > li:nth-child(odd) > .xr-var-name span {\n",
              "  background-color: var(--xr-background-color-row-odd);\n",
              "}\n",
              "\n",
              ".xr-var-name {\n",
              "  grid-column: 1;\n",
              "}\n",
              "\n",
              ".xr-var-dims {\n",
              "  grid-column: 2;\n",
              "}\n",
              "\n",
              ".xr-var-dtype {\n",
              "  grid-column: 3;\n",
              "  text-align: right;\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-var-preview {\n",
              "  grid-column: 4;\n",
              "}\n",
              "\n",
              ".xr-var-name,\n",
              ".xr-var-dims,\n",
              ".xr-var-dtype,\n",
              ".xr-preview,\n",
              ".xr-attrs dt {\n",
              "  white-space: nowrap;\n",
              "  overflow: hidden;\n",
              "  text-overflow: ellipsis;\n",
              "  padding-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-var-name:hover,\n",
              ".xr-var-dims:hover,\n",
              ".xr-var-dtype:hover,\n",
              ".xr-attrs dt:hover {\n",
              "  overflow: visible;\n",
              "  width: auto;\n",
              "  z-index: 1;\n",
              "}\n",
              "\n",
              ".xr-var-attrs,\n",
              ".xr-var-data {\n",
              "  display: none;\n",
              "  background-color: var(--xr-background-color) !important;\n",
              "  padding-bottom: 5px !important;\n",
              "}\n",
              "\n",
              ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
              ".xr-var-data-in:checked ~ .xr-var-data {\n",
              "  display: block;\n",
              "}\n",
              "\n",
              ".xr-var-data > table {\n",
              "  float: right;\n",
              "}\n",
              "\n",
              ".xr-var-name span,\n",
              ".xr-var-data,\n",
              ".xr-attrs {\n",
              "  padding-left: 25px !important;\n",
              "}\n",
              "\n",
              ".xr-attrs,\n",
              ".xr-var-attrs,\n",
              ".xr-var-data {\n",
              "  grid-column: 1 / -1;\n",
              "}\n",
              "\n",
              "dl.xr-attrs {\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "  display: grid;\n",
              "  grid-template-columns: 125px auto;\n",
              "}\n",
              "\n",
              ".xr-attrs dt,\n",
              ".xr-attrs dd {\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "  float: left;\n",
              "  padding-right: 10px;\n",
              "  width: auto;\n",
              "}\n",
              "\n",
              ".xr-attrs dt {\n",
              "  font-weight: normal;\n",
              "  grid-column: 1;\n",
              "}\n",
              "\n",
              ".xr-attrs dt:hover span {\n",
              "  display: inline-block;\n",
              "  background: var(--xr-background-color);\n",
              "  padding-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-attrs dd {\n",
              "  grid-column: 2;\n",
              "  white-space: pre-wrap;\n",
              "  word-break: break-all;\n",
              "}\n",
              "\n",
              ".xr-icon-database,\n",
              ".xr-icon-file-text2 {\n",
              "  display: inline-block;\n",
              "  vertical-align: middle;\n",
              "  width: 1em;\n",
              "  height: 1.5em !important;\n",
              "  stroke-width: 0;\n",
              "  stroke: currentColor;\n",
              "  fill: currentColor;\n",
              "}\n",
              "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n",
              "Dimensions:              (chain: 2, draw: 1000)\n",
              "Coordinates:\n",
              "  * chain                (chain) int64 0 1\n",
              "  * draw                 (draw) int64 0 1 2 3 4 5 6 ... 994 995 996 997 998 999\n",
              "Data variables: (12/16)\n",
              "    diverging            (chain, draw) bool False False False ... False False\n",
              "    energy               (chain, draw) float64 -1.024e+04 ... -1.115e+04\n",
              "    lp                   (chain, draw) float64 1.068e+04 1.071e+04 ... 1.158e+04\n",
              "    largest_eigval       (chain, draw) float64 nan nan nan nan ... nan nan nan\n",
              "    max_energy_error     (chain, draw) float64 -0.6601 -0.5694 ... 0.7473 1.19\n",
              "    acceptance_rate      (chain, draw) float64 0.9988 0.9769 ... 0.8448 0.6552\n",
              "    ...                   ...\n",
              "    perf_counter_diff    (chain, draw) float64 0.01661 0.01658 ... 0.02945\n",
              "    index_in_trajectory  (chain, draw) int64 22 14 19 6 9 ... -20 -1 -14 22 -1\n",
              "    energy_error         (chain, draw) float64 -0.3127 -0.5694 ... 0.5296\n",
              "    smallest_eigval      (chain, draw) float64 nan nan nan nan ... nan nan nan\n",
              "    process_time_diff    (chain, draw) float64 0.01662 0.01657 ... 0.03019\n",
              "    perf_counter_start   (chain, draw) float64 1.341e+03 1.341e+03 ... 1.425e+03\n",
              "Attributes:\n",
              "    created_at:                 2022-10-05T04:33:10.852372\n",
              "    arviz_version:              0.12.1\n",
              "    inference_library:          pymc\n",
              "    inference_library_version:  4.1.4\n",
              "    sampling_time:              122.29010105133057\n",
              "    tuning_steps:               1000</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-fe658328-a94d-4af0-8b90-61a4ec5d8fe6' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-fe658328-a94d-4af0-8b90-61a4ec5d8fe6' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>chain</span>: 2</li><li><span class='xr-has-index'>draw</span>: 1000</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-e1356273-139c-409b-becd-e94f1f3c4b2d' class='xr-section-summary-in' type='checkbox'  checked><label for='section-e1356273-139c-409b-becd-e94f1f3c4b2d' class='xr-section-summary' >Coordinates: <span>(2)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>chain</span></div><div class='xr-var-dims'>(chain)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1</div><input id='attrs-6b6b562e-0ce4-46a5-bbe4-2d8d7151e11e' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-6b6b562e-0ce4-46a5-bbe4-2d8d7151e11e' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-e3a530a6-3880-4296-a631-e7cdf2b63cd2' class='xr-var-data-in' type='checkbox'><label for='data-e3a530a6-3880-4296-a631-e7cdf2b63cd2' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0, 1])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>draw</span></div><div class='xr-var-dims'>(draw)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 5 ... 995 996 997 998 999</div><input id='attrs-039b7b4d-54e6-4565-8cab-4ed7f7217416' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-039b7b4d-54e6-4565-8cab-4ed7f7217416' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-2c866491-0bf6-4642-9320-4b25aaf11750' class='xr-var-data-in' type='checkbox'><label for='data-2c866491-0bf6-4642-9320-4b25aaf11750' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([  0,   1,   2, ..., 997, 998, 999])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-1d1f4602-ebe2-435b-9f9d-e39da3f02168' class='xr-section-summary-in' type='checkbox'  ><label for='section-1d1f4602-ebe2-435b-9f9d-e39da3f02168' class='xr-section-summary' >Data variables: <span>(16)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>diverging</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>bool</div><div class='xr-var-preview xr-preview'>False False False ... False False</div><input id='attrs-3ee38cfe-44c8-496a-b992-0ccac80dcb3f' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-3ee38cfe-44c8-496a-b992-0ccac80dcb3f' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-c44134a4-8be0-4baa-9f12-a52b6bd1b6f8' class='xr-var-data-in' type='checkbox'><label for='data-c44134a4-8be0-4baa-9f12-a52b6bd1b6f8' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[False, False, False, ..., False, False, False],\n",
              "       [False, False, False, ..., False, False, False]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>energy</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>-1.024e+04 ... -1.115e+04</div><input id='attrs-038ef001-efd6-431c-a0c2-cd77dbe19b27' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-038ef001-efd6-431c-a0c2-cd77dbe19b27' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-8723d062-8861-40dd-aff6-387c1ee04961' class='xr-var-data-in' type='checkbox'><label for='data-8723d062-8861-40dd-aff6-387c1ee04961' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[-10242.22210856, -10260.99579072, -10267.06352669, ...,\n",
              "        -10330.80176039, -10362.21264024, -10365.05453275],\n",
              "       [-10713.86760458, -10706.07060981, -10705.25516931, ...,\n",
              "        -11161.20433259, -11123.12525167, -11152.4709883 ]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>lp</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>1.068e+04 1.071e+04 ... 1.158e+04</div><input id='attrs-d0706485-15d9-414d-86a9-7c908ade955f' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-d0706485-15d9-414d-86a9-7c908ade955f' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-af1f56d4-c673-4aa2-9366-2a28f0889826' class='xr-var-data-in' type='checkbox'><label for='data-af1f56d4-c673-4aa2-9366-2a28f0889826' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[10678.14586661, 10707.37358759, 10691.20387175, ...,\n",
              "        10768.17645061, 10798.33798929, 10833.21604789],\n",
              "       [11171.682056  , 11135.96553094, 11158.0384219 , ...,\n",
              "        11564.27168638, 11576.84583085, 11578.85375057]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>largest_eigval</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>nan nan nan nan ... nan nan nan nan</div><input id='attrs-e55aee56-d12a-4592-945e-31d3222a5c76' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-e55aee56-d12a-4592-945e-31d3222a5c76' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-12cff4bb-fa59-4ed1-ae43-4334abd4b56b' class='xr-var-data-in' type='checkbox'><label for='data-12cff4bb-fa59-4ed1-ae43-4334abd4b56b' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[nan, nan, nan, ..., nan, nan, nan],\n",
              "       [nan, nan, nan, ..., nan, nan, nan]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>max_energy_error</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>-0.6601 -0.5694 ... 0.7473 1.19</div><input id='attrs-65056600-111c-4f85-a82b-d67aae94f024' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-65056600-111c-4f85-a82b-d67aae94f024' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-01297b97-dab1-48e7-bfeb-7bca37a05f89' class='xr-var-data-in' type='checkbox'><label for='data-01297b97-dab1-48e7-bfeb-7bca37a05f89' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[-0.6600521 , -0.56940129,  0.75114063, ..., -0.70051541,\n",
              "        -0.54422089, -0.9192551 ],\n",
              "       [-0.18728894,  0.32434854,  0.25688376, ..., -0.66586752,\n",
              "         0.747298  ,  1.19023409]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>acceptance_rate</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.9988 0.9769 ... 0.8448 0.6552</div><input id='attrs-5e9181b0-5869-4525-a9c3-6ee445161549' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-5e9181b0-5869-4525-a9c3-6ee445161549' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-ba1ffe02-0829-4acb-b880-3ef88da2d419' class='xr-var-data-in' type='checkbox'><label for='data-ba1ffe02-0829-4acb-b880-3ef88da2d419' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[0.99880023, 0.97688778, 0.7050917 , ..., 0.91032404, 0.97429855,\n",
              "        0.94623747],\n",
              "       [0.99127995, 0.85010645, 0.90481802, ..., 0.93576197, 0.84479651,\n",
              "        0.65518069]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>step_size</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.1008 0.1008 ... 0.1079 0.1079</div><input id='attrs-3ca5e924-32f2-4a16-a926-441db84b543e' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-3ca5e924-32f2-4a16-a926-441db84b543e' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-4707c301-1d3c-4cbe-be81-f4bd69f5fa53' class='xr-var-data-in' type='checkbox'><label for='data-4707c301-1d3c-4cbe-be81-f4bd69f5fa53' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[0.10078243, 0.10078243, 0.10078243, ..., 0.10078243, 0.10078243,\n",
              "        0.10078243],\n",
              "       [0.10790039, 0.10790039, 0.10790039, ..., 0.10790039, 0.10790039,\n",
              "        0.10790039]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>n_steps</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>31.0 31.0 31.0 ... 31.0 31.0 31.0</div><input id='attrs-7f00c045-bdf5-4237-8e2d-d3fdb4c67e97' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-7f00c045-bdf5-4237-8e2d-d3fdb4c67e97' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-a99d32cc-a8a3-4e18-92a5-a384e028a8d4' class='xr-var-data-in' type='checkbox'><label for='data-a99d32cc-a8a3-4e18-92a5-a384e028a8d4' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[31., 31., 31., ..., 31., 31., 31.],\n",
              "       [63., 63., 63., ..., 31., 31., 31.]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>step_size_bar</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.08996 0.08996 ... 0.06956 0.06956</div><input id='attrs-9698b94e-3c9a-4577-a411-5d48619cf44f' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-9698b94e-3c9a-4577-a411-5d48619cf44f' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-205e77ab-d0b4-47bb-b1e3-db75f6677d84' class='xr-var-data-in' type='checkbox'><label for='data-205e77ab-d0b4-47bb-b1e3-db75f6677d84' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[0.08995522, 0.08995522, 0.08995522, ..., 0.08995522, 0.08995522,\n",
              "        0.08995522],\n",
              "       [0.06955748, 0.06955748, 0.06955748, ..., 0.06955748, 0.06955748,\n",
              "        0.06955748]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>tree_depth</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>5 5 5 5 5 5 5 5 ... 5 5 5 5 5 5 5 5</div><input id='attrs-c61582fe-4c70-4d3c-bf38-bdd023936e26' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-c61582fe-4c70-4d3c-bf38-bdd023936e26' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-938c1520-60d0-4e72-89a9-791ee6d5d5a6' class='xr-var-data-in' type='checkbox'><label for='data-938c1520-60d0-4e72-89a9-791ee6d5d5a6' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[5, 5, 5, ..., 5, 5, 5],\n",
              "       [6, 6, 6, ..., 5, 5, 5]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>perf_counter_diff</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.01661 0.01658 ... 0.01722 0.02945</div><input id='attrs-75a52a5c-0917-4218-bee7-d66ab2aff1d7' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-75a52a5c-0917-4218-bee7-d66ab2aff1d7' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-803d72c6-49eb-478c-9327-392f0eb360f7' class='xr-var-data-in' type='checkbox'><label for='data-803d72c6-49eb-478c-9327-392f0eb360f7' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[0.016614  , 0.01657529, 0.01700417, ..., 0.01691942, 0.01673833,\n",
              "        0.01659839],\n",
              "       [0.03536138, 0.04575161, 0.03377729, ..., 0.01779343, 0.01722343,\n",
              "        0.02945363]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>index_in_trajectory</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>22 14 19 6 9 ... -20 -1 -14 22 -1</div><input id='attrs-a2e3024a-4e4c-43f8-861c-c6c61ec06eba' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-a2e3024a-4e4c-43f8-861c-c6c61ec06eba' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-95002529-9158-4d75-937d-02eb0f15096b' class='xr-var-data-in' type='checkbox'><label for='data-95002529-9158-4d75-937d-02eb0f15096b' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[ 22,  14,  19, ...,  12, -11, -27],\n",
              "       [-31,  41, -11, ..., -14,  22,  -1]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>energy_error</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>-0.3127 -0.5694 ... -0.1356 0.5296</div><input id='attrs-4b6026bd-8543-4137-9c43-f7a6f0662e8e' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-4b6026bd-8543-4137-9c43-f7a6f0662e8e' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-080a72b6-05e4-4af6-9cea-2ac3f93ac554' class='xr-var-data-in' type='checkbox'><label for='data-080a72b6-05e4-4af6-9cea-2ac3f93ac554' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[-0.31266521, -0.56940129,  0.66709423, ..., -0.32979531,\n",
              "        -0.12665489, -0.9192551 ],\n",
              "       [-0.15354384,  0.15821938,  0.01855493, ..., -0.1086977 ,\n",
              "        -0.13556762,  0.52961798]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>smallest_eigval</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>nan nan nan nan ... nan nan nan nan</div><input id='attrs-58a44df1-51b4-4d4c-b7fd-d89de376f418' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-58a44df1-51b4-4d4c-b7fd-d89de376f418' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-2da1599f-7684-49b3-a96f-a2fde3aec8bd' class='xr-var-data-in' type='checkbox'><label for='data-2da1599f-7684-49b3-a96f-a2fde3aec8bd' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[nan, nan, nan, ..., nan, nan, nan],\n",
              "       [nan, nan, nan, ..., nan, nan, nan]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>process_time_diff</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.01662 0.01657 ... 0.01713 0.03019</div><input id='attrs-1a9b319a-778c-4298-a021-1512b04d3db1' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-1a9b319a-778c-4298-a021-1512b04d3db1' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-ac88f121-958d-4a3d-b12c-0d1cecb86ad7' class='xr-var-data-in' type='checkbox'><label for='data-ac88f121-958d-4a3d-b12c-0d1cecb86ad7' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[0.01661512, 0.01656506, 0.01699134, ..., 0.01686638, 0.01674157,\n",
              "        0.01660327],\n",
              "       [0.0352701 , 0.0496942 , 0.03376219, ..., 0.01793374, 0.01712572,\n",
              "        0.03019241]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>perf_counter_start</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>1.341e+03 1.341e+03 ... 1.425e+03</div><input id='attrs-2454c476-8c49-4fb5-9d4b-6386301aab1b' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-2454c476-8c49-4fb5-9d4b-6386301aab1b' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-64ecc11b-cf16-4e04-a9d1-2c23fbd0844d' class='xr-var-data-in' type='checkbox'><label for='data-64ecc11b-cf16-4e04-a9d1-2c23fbd0844d' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[1341.18067202, 1341.19767339, 1341.21461439, ..., 1364.69959185,\n",
              "        1364.71692939, 1364.73408361],\n",
              "       [1397.49650339, 1397.53224812, 1397.57839711, ..., 1424.97933182,\n",
              "        1424.99781397, 1425.01849344]])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-7f1d18b0-308b-46e4-9f7b-ba292579534c' class='xr-section-summary-in' type='checkbox'  checked><label for='section-7f1d18b0-308b-46e4-9f7b-ba292579534c' class='xr-section-summary' >Attributes: <span>(6)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>created_at :</span></dt><dd>2022-10-05T04:33:10.852372</dd><dt><span>arviz_version :</span></dt><dd>0.12.1</dd><dt><span>inference_library :</span></dt><dd>pymc</dd><dt><span>inference_library_version :</span></dt><dd>4.1.4</dd><dt><span>sampling_time :</span></dt><dd>122.29010105133057</dd><dt><span>tuning_steps :</span></dt><dd>1000</dd></dl></div></li></ul></div></div><br></div>\n",
              "                      </ul>\n",
              "                  </div>\n",
              "            </li>\n",
              "            \n",
              "            <li class = \"xr-section-item\">\n",
              "                  <input id=\"idata_observed_data464b090d-6d9b-4e8e-b757-89156d736577\" class=\"xr-section-summary-in\" type=\"checkbox\">\n",
              "                  <label for=\"idata_observed_data464b090d-6d9b-4e8e-b757-89156d736577\" class = \"xr-section-summary\">observed_data</label>\n",
              "                  <div class=\"xr-section-inline-details\"></div>\n",
              "                  <div class=\"xr-section-details\">\n",
              "                      <ul id=\"xr-dataset-coord-list\" class=\"xr-var-list\">\n",
              "                          <div style=\"padding-left:2rem;\"><div><svg style=\"position: absolute; width: 0; height: 0; overflow: hidden\">\n",
              "<defs>\n",
              "<symbol id=\"icon-database\" viewBox=\"0 0 32 32\">\n",
              "<path d=\"M16 0c-8.837 0-16 2.239-16 5v4c0 2.761 7.163 5 16 5s16-2.239 16-5v-4c0-2.761-7.163-5-16-5z\"></path>\n",
              "<path d=\"M16 17c-8.837 0-16-2.239-16-5v6c0 2.761 7.163 5 16 5s16-2.239 16-5v-6c0 2.761-7.163 5-16 5z\"></path>\n",
              "<path d=\"M16 26c-8.837 0-16-2.239-16-5v6c0 2.761 7.163 5 16 5s16-2.239 16-5v-6c0 2.761-7.163 5-16 5z\"></path>\n",
              "</symbol>\n",
              "<symbol id=\"icon-file-text2\" viewBox=\"0 0 32 32\">\n",
              "<path d=\"M28.681 7.159c-0.694-0.947-1.662-2.053-2.724-3.116s-2.169-2.030-3.116-2.724c-1.612-1.182-2.393-1.319-2.841-1.319h-15.5c-1.378 0-2.5 1.121-2.5 2.5v27c0 1.378 1.122 2.5 2.5 2.5h23c1.378 0 2.5-1.122 2.5-2.5v-19.5c0-0.448-0.137-1.23-1.319-2.841zM24.543 5.457c0.959 0.959 1.712 1.825 2.268 2.543h-4.811v-4.811c0.718 0.556 1.584 1.309 2.543 2.268zM28 29.5c0 0.271-0.229 0.5-0.5 0.5h-23c-0.271 0-0.5-0.229-0.5-0.5v-27c0-0.271 0.229-0.5 0.5-0.5 0 0 15.499-0 15.5 0v7c0 0.552 0.448 1 1 1h7v19.5z\"></path>\n",
              "<path d=\"M23 26h-14c-0.552 0-1-0.448-1-1s0.448-1 1-1h14c0.552 0 1 0.448 1 1s-0.448 1-1 1z\"></path>\n",
              "<path d=\"M23 22h-14c-0.552 0-1-0.448-1-1s0.448-1 1-1h14c0.552 0 1 0.448 1 1s-0.448 1-1 1z\"></path>\n",
              "<path d=\"M23 18h-14c-0.552 0-1-0.448-1-1s0.448-1 1-1h14c0.552 0 1 0.448 1 1s-0.448 1-1 1z\"></path>\n",
              "</symbol>\n",
              "</defs>\n",
              "</svg>\n",
              "<style>/* CSS stylesheet for displaying xarray objects in jupyterlab.\n",
              " *\n",
              " */\n",
              "\n",
              ":root {\n",
              "  --xr-font-color0: var(--jp-content-font-color0, rgba(0, 0, 0, 1));\n",
              "  --xr-font-color2: var(--jp-content-font-color2, rgba(0, 0, 0, 0.54));\n",
              "  --xr-font-color3: var(--jp-content-font-color3, rgba(0, 0, 0, 0.38));\n",
              "  --xr-border-color: var(--jp-border-color2, #e0e0e0);\n",
              "  --xr-disabled-color: var(--jp-layout-color3, #bdbdbd);\n",
              "  --xr-background-color: var(--jp-layout-color0, white);\n",
              "  --xr-background-color-row-even: var(--jp-layout-color1, white);\n",
              "  --xr-background-color-row-odd: var(--jp-layout-color2, #eeeeee);\n",
              "}\n",
              "\n",
              "html[theme=dark],\n",
              "body.vscode-dark {\n",
              "  --xr-font-color0: rgba(255, 255, 255, 1);\n",
              "  --xr-font-color2: rgba(255, 255, 255, 0.54);\n",
              "  --xr-font-color3: rgba(255, 255, 255, 0.38);\n",
              "  --xr-border-color: #1F1F1F;\n",
              "  --xr-disabled-color: #515151;\n",
              "  --xr-background-color: #111111;\n",
              "  --xr-background-color-row-even: #111111;\n",
              "  --xr-background-color-row-odd: #313131;\n",
              "}\n",
              "\n",
              ".xr-wrap {\n",
              "  display: block !important;\n",
              "  min-width: 300px;\n",
              "  max-width: 700px;\n",
              "}\n",
              "\n",
              ".xr-text-repr-fallback {\n",
              "  /* fallback to plain text repr when CSS is not injected (untrusted notebook) */\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-header {\n",
              "  padding-top: 6px;\n",
              "  padding-bottom: 6px;\n",
              "  margin-bottom: 4px;\n",
              "  border-bottom: solid 1px var(--xr-border-color);\n",
              "}\n",
              "\n",
              ".xr-header > div,\n",
              ".xr-header > ul {\n",
              "  display: inline;\n",
              "  margin-top: 0;\n",
              "  margin-bottom: 0;\n",
              "}\n",
              "\n",
              ".xr-obj-type,\n",
              ".xr-array-name {\n",
              "  margin-left: 2px;\n",
              "  margin-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-obj-type {\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-sections {\n",
              "  padding-left: 0 !important;\n",
              "  display: grid;\n",
              "  grid-template-columns: 150px auto auto 1fr 20px 20px;\n",
              "}\n",
              "\n",
              ".xr-section-item {\n",
              "  display: contents;\n",
              "}\n",
              "\n",
              ".xr-section-item input {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-section-item input + label {\n",
              "  color: var(--xr-disabled-color);\n",
              "}\n",
              "\n",
              ".xr-section-item input:enabled + label {\n",
              "  cursor: pointer;\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-section-item input:enabled + label:hover {\n",
              "  color: var(--xr-font-color0);\n",
              "}\n",
              "\n",
              ".xr-section-summary {\n",
              "  grid-column: 1;\n",
              "  color: var(--xr-font-color2);\n",
              "  font-weight: 500;\n",
              "}\n",
              "\n",
              ".xr-section-summary > span {\n",
              "  display: inline-block;\n",
              "  padding-left: 0.5em;\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:disabled + label {\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-section-summary-in + label:before {\n",
              "  display: inline-block;\n",
              "  content: '►';\n",
              "  font-size: 11px;\n",
              "  width: 15px;\n",
              "  text-align: center;\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:disabled + label:before {\n",
              "  color: var(--xr-disabled-color);\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:checked + label:before {\n",
              "  content: '▼';\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:checked + label > span {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-section-summary,\n",
              ".xr-section-inline-details {\n",
              "  padding-top: 4px;\n",
              "  padding-bottom: 4px;\n",
              "}\n",
              "\n",
              ".xr-section-inline-details {\n",
              "  grid-column: 2 / -1;\n",
              "}\n",
              "\n",
              ".xr-section-details {\n",
              "  display: none;\n",
              "  grid-column: 1 / -1;\n",
              "  margin-bottom: 5px;\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:checked ~ .xr-section-details {\n",
              "  display: contents;\n",
              "}\n",
              "\n",
              ".xr-array-wrap {\n",
              "  grid-column: 1 / -1;\n",
              "  display: grid;\n",
              "  grid-template-columns: 20px auto;\n",
              "}\n",
              "\n",
              ".xr-array-wrap > label {\n",
              "  grid-column: 1;\n",
              "  vertical-align: top;\n",
              "}\n",
              "\n",
              ".xr-preview {\n",
              "  color: var(--xr-font-color3);\n",
              "}\n",
              "\n",
              ".xr-array-preview,\n",
              ".xr-array-data {\n",
              "  padding: 0 5px !important;\n",
              "  grid-column: 2;\n",
              "}\n",
              "\n",
              ".xr-array-data,\n",
              ".xr-array-in:checked ~ .xr-array-preview {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-array-in:checked ~ .xr-array-data,\n",
              ".xr-array-preview {\n",
              "  display: inline-block;\n",
              "}\n",
              "\n",
              ".xr-dim-list {\n",
              "  display: inline-block !important;\n",
              "  list-style: none;\n",
              "  padding: 0 !important;\n",
              "  margin: 0;\n",
              "}\n",
              "\n",
              ".xr-dim-list li {\n",
              "  display: inline-block;\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "}\n",
              "\n",
              ".xr-dim-list:before {\n",
              "  content: '(';\n",
              "}\n",
              "\n",
              ".xr-dim-list:after {\n",
              "  content: ')';\n",
              "}\n",
              "\n",
              ".xr-dim-list li:not(:last-child):after {\n",
              "  content: ',';\n",
              "  padding-right: 5px;\n",
              "}\n",
              "\n",
              ".xr-has-index {\n",
              "  font-weight: bold;\n",
              "}\n",
              "\n",
              ".xr-var-list,\n",
              ".xr-var-item {\n",
              "  display: contents;\n",
              "}\n",
              "\n",
              ".xr-var-item > div,\n",
              ".xr-var-item label,\n",
              ".xr-var-item > .xr-var-name span {\n",
              "  background-color: var(--xr-background-color-row-even);\n",
              "  margin-bottom: 0;\n",
              "}\n",
              "\n",
              ".xr-var-item > .xr-var-name:hover span {\n",
              "  padding-right: 5px;\n",
              "}\n",
              "\n",
              ".xr-var-list > li:nth-child(odd) > div,\n",
              ".xr-var-list > li:nth-child(odd) > label,\n",
              ".xr-var-list > li:nth-child(odd) > .xr-var-name span {\n",
              "  background-color: var(--xr-background-color-row-odd);\n",
              "}\n",
              "\n",
              ".xr-var-name {\n",
              "  grid-column: 1;\n",
              "}\n",
              "\n",
              ".xr-var-dims {\n",
              "  grid-column: 2;\n",
              "}\n",
              "\n",
              ".xr-var-dtype {\n",
              "  grid-column: 3;\n",
              "  text-align: right;\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-var-preview {\n",
              "  grid-column: 4;\n",
              "}\n",
              "\n",
              ".xr-var-name,\n",
              ".xr-var-dims,\n",
              ".xr-var-dtype,\n",
              ".xr-preview,\n",
              ".xr-attrs dt {\n",
              "  white-space: nowrap;\n",
              "  overflow: hidden;\n",
              "  text-overflow: ellipsis;\n",
              "  padding-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-var-name:hover,\n",
              ".xr-var-dims:hover,\n",
              ".xr-var-dtype:hover,\n",
              ".xr-attrs dt:hover {\n",
              "  overflow: visible;\n",
              "  width: auto;\n",
              "  z-index: 1;\n",
              "}\n",
              "\n",
              ".xr-var-attrs,\n",
              ".xr-var-data {\n",
              "  display: none;\n",
              "  background-color: var(--xr-background-color) !important;\n",
              "  padding-bottom: 5px !important;\n",
              "}\n",
              "\n",
              ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
              ".xr-var-data-in:checked ~ .xr-var-data {\n",
              "  display: block;\n",
              "}\n",
              "\n",
              ".xr-var-data > table {\n",
              "  float: right;\n",
              "}\n",
              "\n",
              ".xr-var-name span,\n",
              ".xr-var-data,\n",
              ".xr-attrs {\n",
              "  padding-left: 25px !important;\n",
              "}\n",
              "\n",
              ".xr-attrs,\n",
              ".xr-var-attrs,\n",
              ".xr-var-data {\n",
              "  grid-column: 1 / -1;\n",
              "}\n",
              "\n",
              "dl.xr-attrs {\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "  display: grid;\n",
              "  grid-template-columns: 125px auto;\n",
              "}\n",
              "\n",
              ".xr-attrs dt,\n",
              ".xr-attrs dd {\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "  float: left;\n",
              "  padding-right: 10px;\n",
              "  width: auto;\n",
              "}\n",
              "\n",
              ".xr-attrs dt {\n",
              "  font-weight: normal;\n",
              "  grid-column: 1;\n",
              "}\n",
              "\n",
              ".xr-attrs dt:hover span {\n",
              "  display: inline-block;\n",
              "  background: var(--xr-background-color);\n",
              "  padding-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-attrs dd {\n",
              "  grid-column: 2;\n",
              "  white-space: pre-wrap;\n",
              "  word-break: break-all;\n",
              "}\n",
              "\n",
              ".xr-icon-database,\n",
              ".xr-icon-file-text2 {\n",
              "  display: inline-block;\n",
              "  vertical-align: middle;\n",
              "  width: 1em;\n",
              "  height: 1.5em !important;\n",
              "  stroke-width: 0;\n",
              "  stroke: currentColor;\n",
              "  fill: currentColor;\n",
              "}\n",
              "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n",
              "Dimensions:  (subject: 420, measure: 6)\n",
              "Coordinates:\n",
              "  * subject  (subject) int64 0 1 2 3 4 5 6 7 ... 412 413 414 415 416 417 418 419\n",
              "  * measure  (measure) &lt;U2 &#x27;lr&#x27; &#x27;la&#x27; &#x27;af&#x27; &#x27;pr&#x27; &#x27;gn&#x27; &#x27;fb&#x27;\n",
              "Data variables:\n",
              "    obs_y    (subject, measure) float64 0.5875 0.8914 0.9984 ... 0.5387 0.5518\n",
              "Attributes:\n",
              "    created_at:                 2022-10-05T04:33:13.059564\n",
              "    arviz_version:              0.12.1\n",
              "    inference_library:          pymc\n",
              "    inference_library_version:  4.1.4</pre><div class='xr-wrap' style='display:none'><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-6f444b48-7c22-422b-b2d3-c1d32034e270' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-6f444b48-7c22-422b-b2d3-c1d32034e270' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>subject</span>: 420</li><li><span class='xr-has-index'>measure</span>: 6</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-ddfd1cbe-cfba-4ddb-b130-2abb2b1c32bd' class='xr-section-summary-in' type='checkbox'  checked><label for='section-ddfd1cbe-cfba-4ddb-b130-2abb2b1c32bd' class='xr-section-summary' >Coordinates: <span>(2)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>subject</span></div><div class='xr-var-dims'>(subject)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 5 ... 415 416 417 418 419</div><input id='attrs-efd833a3-b48d-4fa2-bca9-4ccff12affad' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-efd833a3-b48d-4fa2-bca9-4ccff12affad' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-d53957a6-9280-4c5a-ba8d-508ee26680ee' class='xr-var-data-in' type='checkbox'><label for='data-d53957a6-9280-4c5a-ba8d-508ee26680ee' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([  0,   1,   2, ..., 417, 418, 419])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>measure</span></div><div class='xr-var-dims'>(measure)</div><div class='xr-var-dtype'>&lt;U2</div><div class='xr-var-preview xr-preview'>&#x27;lr&#x27; &#x27;la&#x27; &#x27;af&#x27; &#x27;pr&#x27; &#x27;gn&#x27; &#x27;fb&#x27;</div><input id='attrs-89c234b5-51f2-4472-a054-04fe836b6565' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-89c234b5-51f2-4472-a054-04fe836b6565' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-b8d63fd5-f743-421c-a4be-ba8eda5b6a8f' class='xr-var-data-in' type='checkbox'><label for='data-b8d63fd5-f743-421c-a4be-ba8eda5b6a8f' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([&#x27;lr&#x27;, &#x27;la&#x27;, &#x27;af&#x27;, &#x27;pr&#x27;, &#x27;gn&#x27;, &#x27;fb&#x27;], dtype=&#x27;&lt;U2&#x27;)</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-4e5a16c2-a94f-45e3-a8b2-a09c2d97e635' class='xr-section-summary-in' type='checkbox'  checked><label for='section-4e5a16c2-a94f-45e3-a8b2-a09c2d97e635' class='xr-section-summary' >Data variables: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>obs_y</span></div><div class='xr-var-dims'>(subject, measure)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>0.5875 0.8914 ... 0.5387 0.5518</div><input id='attrs-70cdc693-5ddc-46c7-8ce3-9f1b961e907b' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-70cdc693-5ddc-46c7-8ce3-9f1b961e907b' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-d1033855-fb81-4cbb-84f6-2108e0819897' class='xr-var-data-in' type='checkbox'><label for='data-d1033855-fb81-4cbb-84f6-2108e0819897' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[0.58745738, 0.89143834, 0.99841825, 0.55516259, 0.90892034,\n",
              "        1.01334973],\n",
              "       [0.61090499, 0.87693303, 1.02606788, 0.55285554, 0.91971058,\n",
              "        1.02299606],\n",
              "       [0.58467809, 0.86849213, 1.02582435, 0.56662364, 0.91086095,\n",
              "        1.02730253],\n",
              "       ...,\n",
              "       [0.52921523, 0.52824928, 0.53039445, 0.53847279, 0.52928731,\n",
              "        0.53964574],\n",
              "       [0.52374974, 0.52448948, 0.55099746, 0.52102334, 0.5424217 ,\n",
              "        0.5170661 ],\n",
              "       [0.53869954, 0.54275446, 0.54709638, 0.52637621, 0.53867731,\n",
              "        0.55178501]])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-c26c06b1-dc43-4310-9c5f-191c3f54161e' class='xr-section-summary-in' type='checkbox'  checked><label for='section-c26c06b1-dc43-4310-9c5f-191c3f54161e' class='xr-section-summary' >Attributes: <span>(4)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>created_at :</span></dt><dd>2022-10-05T04:33:13.059564</dd><dt><span>arviz_version :</span></dt><dd>0.12.1</dd><dt><span>inference_library :</span></dt><dd>pymc</dd><dt><span>inference_library_version :</span></dt><dd>4.1.4</dd></dl></div></li></ul></div></div><br></div>\n",
              "                      </ul>\n",
              "                  </div>\n",
              "            </li>\n",
              "            \n",
              "              </ul>\n",
              "            </div>\n",
              "            <style> /* CSS stylesheet for displaying InferenceData objects in jupyterlab.\n",
              " *\n",
              " */\n",
              "\n",
              ":root {\n",
              "  --xr-font-color0: var(--jp-content-font-color0, rgba(0, 0, 0, 1));\n",
              "  --xr-font-color2: var(--jp-content-font-color2, rgba(0, 0, 0, 0.54));\n",
              "  --xr-font-color3: var(--jp-content-font-color3, rgba(0, 0, 0, 0.38));\n",
              "  --xr-border-color: var(--jp-border-color2, #e0e0e0);\n",
              "  --xr-disabled-color: var(--jp-layout-color3, #bdbdbd);\n",
              "  --xr-background-color: var(--jp-layout-color0, white);\n",
              "  --xr-background-color-row-even: var(--jp-layout-color1, white);\n",
              "  --xr-background-color-row-odd: var(--jp-layout-color2, #eeeeee);\n",
              "}\n",
              "\n",
              "html[theme=dark],\n",
              "body.vscode-dark {\n",
              "  --xr-font-color0: rgba(255, 255, 255, 1);\n",
              "  --xr-font-color2: rgba(255, 255, 255, 0.54);\n",
              "  --xr-font-color3: rgba(255, 255, 255, 0.38);\n",
              "  --xr-border-color: #1F1F1F;\n",
              "  --xr-disabled-color: #515151;\n",
              "  --xr-background-color: #111111;\n",
              "  --xr-background-color-row-even: #111111;\n",
              "  --xr-background-color-row-odd: #313131;\n",
              "}\n",
              "\n",
              ".xr-wrap {\n",
              "  display: block;\n",
              "  min-width: 300px;\n",
              "  max-width: 700px;\n",
              "}\n",
              "\n",
              ".xr-text-repr-fallback {\n",
              "  /* fallback to plain text repr when CSS is not injected (untrusted notebook) */\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-header {\n",
              "  padding-top: 6px;\n",
              "  padding-bottom: 6px;\n",
              "  margin-bottom: 4px;\n",
              "  border-bottom: solid 1px var(--xr-border-color);\n",
              "}\n",
              "\n",
              ".xr-header > div,\n",
              ".xr-header > ul {\n",
              "  display: inline;\n",
              "  margin-top: 0;\n",
              "  margin-bottom: 0;\n",
              "}\n",
              "\n",
              ".xr-obj-type,\n",
              ".xr-array-name {\n",
              "  margin-left: 2px;\n",
              "  margin-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-obj-type {\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-sections {\n",
              "  padding-left: 0 !important;\n",
              "  display: grid;\n",
              "  grid-template-columns: 150px auto auto 1fr 20px 20px;\n",
              "}\n",
              "\n",
              ".xr-sections.group-sections {\n",
              "  grid-template-columns: auto;\n",
              "}\n",
              "\n",
              ".xr-section-item {\n",
              "  display: contents;\n",
              "}\n",
              "\n",
              ".xr-section-item input {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-section-item input + label {\n",
              "  color: var(--xr-disabled-color);\n",
              "}\n",
              "\n",
              ".xr-section-item input:enabled + label {\n",
              "  cursor: pointer;\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-section-item input:enabled + label:hover {\n",
              "  color: var(--xr-font-color0);\n",
              "}\n",
              "\n",
              ".xr-section-summary {\n",
              "  grid-column: 1;\n",
              "  color: var(--xr-font-color2);\n",
              "  font-weight: 500;\n",
              "}\n",
              "\n",
              ".xr-section-summary > span {\n",
              "  display: inline-block;\n",
              "  padding-left: 0.5em;\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:disabled + label {\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-section-summary-in + label:before {\n",
              "  display: inline-block;\n",
              "  content: '►';\n",
              "  font-size: 11px;\n",
              "  width: 15px;\n",
              "  text-align: center;\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:disabled + label:before {\n",
              "  color: var(--xr-disabled-color);\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:checked + label:before {\n",
              "  content: '▼';\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:checked + label > span {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-section-summary,\n",
              ".xr-section-inline-details {\n",
              "  padding-top: 4px;\n",
              "  padding-bottom: 4px;\n",
              "}\n",
              "\n",
              ".xr-section-inline-details {\n",
              "  grid-column: 2 / -1;\n",
              "}\n",
              "\n",
              ".xr-section-details {\n",
              "  display: none;\n",
              "  grid-column: 1 / -1;\n",
              "  margin-bottom: 5px;\n",
              "}\n",
              "\n",
              ".xr-section-summary-in:checked ~ .xr-section-details {\n",
              "  display: contents;\n",
              "}\n",
              "\n",
              ".xr-array-wrap {\n",
              "  grid-column: 1 / -1;\n",
              "  display: grid;\n",
              "  grid-template-columns: 20px auto;\n",
              "}\n",
              "\n",
              ".xr-array-wrap > label {\n",
              "  grid-column: 1;\n",
              "  vertical-align: top;\n",
              "}\n",
              "\n",
              ".xr-preview {\n",
              "  color: var(--xr-font-color3);\n",
              "}\n",
              "\n",
              ".xr-array-preview,\n",
              ".xr-array-data {\n",
              "  padding: 0 5px !important;\n",
              "  grid-column: 2;\n",
              "}\n",
              "\n",
              ".xr-array-data,\n",
              ".xr-array-in:checked ~ .xr-array-preview {\n",
              "  display: none;\n",
              "}\n",
              "\n",
              ".xr-array-in:checked ~ .xr-array-data,\n",
              ".xr-array-preview {\n",
              "  display: inline-block;\n",
              "}\n",
              "\n",
              ".xr-dim-list {\n",
              "  display: inline-block !important;\n",
              "  list-style: none;\n",
              "  padding: 0 !important;\n",
              "  margin: 0;\n",
              "}\n",
              "\n",
              ".xr-dim-list li {\n",
              "  display: inline-block;\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "}\n",
              "\n",
              ".xr-dim-list:before {\n",
              "  content: '(';\n",
              "}\n",
              "\n",
              ".xr-dim-list:after {\n",
              "  content: ')';\n",
              "}\n",
              "\n",
              ".xr-dim-list li:not(:last-child):after {\n",
              "  content: ',';\n",
              "  padding-right: 5px;\n",
              "}\n",
              "\n",
              ".xr-has-index {\n",
              "  font-weight: bold;\n",
              "}\n",
              "\n",
              ".xr-var-list,\n",
              ".xr-var-item {\n",
              "  display: contents;\n",
              "}\n",
              "\n",
              ".xr-var-item > div,\n",
              ".xr-var-item label,\n",
              ".xr-var-item > .xr-var-name span {\n",
              "  background-color: var(--xr-background-color-row-even);\n",
              "  margin-bottom: 0;\n",
              "}\n",
              "\n",
              ".xr-var-item > .xr-var-name:hover span {\n",
              "  padding-right: 5px;\n",
              "}\n",
              "\n",
              ".xr-var-list > li:nth-child(odd) > div,\n",
              ".xr-var-list > li:nth-child(odd) > label,\n",
              ".xr-var-list > li:nth-child(odd) > .xr-var-name span {\n",
              "  background-color: var(--xr-background-color-row-odd);\n",
              "}\n",
              "\n",
              ".xr-var-name {\n",
              "  grid-column: 1;\n",
              "}\n",
              "\n",
              ".xr-var-dims {\n",
              "  grid-column: 2;\n",
              "}\n",
              "\n",
              ".xr-var-dtype {\n",
              "  grid-column: 3;\n",
              "  text-align: right;\n",
              "  color: var(--xr-font-color2);\n",
              "}\n",
              "\n",
              ".xr-var-preview {\n",
              "  grid-column: 4;\n",
              "}\n",
              "\n",
              ".xr-var-name,\n",
              ".xr-var-dims,\n",
              ".xr-var-dtype,\n",
              ".xr-preview,\n",
              ".xr-attrs dt {\n",
              "  white-space: nowrap;\n",
              "  overflow: hidden;\n",
              "  text-overflow: ellipsis;\n",
              "  padding-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-var-name:hover,\n",
              ".xr-var-dims:hover,\n",
              ".xr-var-dtype:hover,\n",
              ".xr-attrs dt:hover {\n",
              "  overflow: visible;\n",
              "  width: auto;\n",
              "  z-index: 1;\n",
              "}\n",
              "\n",
              ".xr-var-attrs,\n",
              ".xr-var-data {\n",
              "  display: none;\n",
              "  background-color: var(--xr-background-color) !important;\n",
              "  padding-bottom: 5px !important;\n",
              "}\n",
              "\n",
              ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
              ".xr-var-data-in:checked ~ .xr-var-data {\n",
              "  display: block;\n",
              "}\n",
              "\n",
              ".xr-var-data > table {\n",
              "  float: right;\n",
              "}\n",
              "\n",
              ".xr-var-name span,\n",
              ".xr-var-data,\n",
              ".xr-attrs {\n",
              "  padding-left: 25px !important;\n",
              "}\n",
              "\n",
              ".xr-attrs,\n",
              ".xr-var-attrs,\n",
              ".xr-var-data {\n",
              "  grid-column: 1 / -1;\n",
              "}\n",
              "\n",
              "dl.xr-attrs {\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "  display: grid;\n",
              "  grid-template-columns: 125px auto;\n",
              "}\n",
              "\n",
              ".xr-attrs dt, dd {\n",
              "  padding: 0;\n",
              "  margin: 0;\n",
              "  float: left;\n",
              "  padding-right: 10px;\n",
              "  width: auto;\n",
              "}\n",
              "\n",
              ".xr-attrs dt {\n",
              "  font-weight: normal;\n",
              "  grid-column: 1;\n",
              "}\n",
              "\n",
              ".xr-attrs dt:hover span {\n",
              "  display: inline-block;\n",
              "  background: var(--xr-background-color);\n",
              "  padding-right: 10px;\n",
              "}\n",
              "\n",
              ".xr-attrs dd {\n",
              "  grid-column: 2;\n",
              "  white-space: pre-wrap;\n",
              "  word-break: break-all;\n",
              "}\n",
              "\n",
              ".xr-icon-database,\n",
              ".xr-icon-file-text2 {\n",
              "  display: inline-block;\n",
              "  vertical-align: middle;\n",
              "  width: 1em;\n",
              "  height: 1.5em !important;\n",
              "  stroke-width: 0;\n",
              "  stroke: currentColor;\n",
              "  fill: currentColor;\n",
              "}\n",
              ".xr-wrap{width:700px!important;} </style>"
            ]
          },
          "metadata": {},
          "execution_count": 33
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "AyxH3n7sAW5k"
      },
      "outputs": [],
      "source": [
        "with model:\n",
        "  prior_samples = pm.sample_prior_predictive()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "o7cJGcYeGx7D",
        "outputId": "33c8dee0-a89a-4758-ec9c-aebfc6666e74"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "                     mean     sd  hdi_3%  hdi_97%  mcse_mean  mcse_sd  \\\n",
              "beta_0[lr]          0.864  0.091   0.766    0.966      0.064    0.054   \n",
              "beta_0[la]          0.900  0.081   0.814    0.988      0.057    0.048   \n",
              "beta_0[af]          0.919  0.076   0.838    1.001      0.053    0.045   \n",
              "beta_0[pr]          0.858  0.093   0.757    0.962      0.066    0.055   \n",
              "beta_0[gn]          0.906  0.079   0.823    0.992      0.055    0.047   \n",
              "beta_0[fb]          0.918  0.075   0.838    1.000      0.053    0.045   \n",
              "beta[0, lr]         0.186  0.025   0.155    0.216      0.017    0.015   \n",
              "beta[0, la]        -0.014  0.171  -0.188    0.166      0.120    0.102   \n",
              "beta[0, af]        -0.113  0.269  -0.385    0.163      0.190    0.160   \n",
              "beta[0, pr]         0.218  0.056   0.155    0.279      0.039    0.033   \n",
              "beta[0, gn]        -0.046  0.203  -0.253    0.164      0.143    0.121   \n",
              "beta[0, fb]        -0.113  0.268  -0.384    0.161      0.189    0.160   \n",
              "beta[1, lr]        -0.130  0.308  -0.451    0.181      0.217    0.184   \n",
              "beta[1, la]        -0.167  0.108  -0.289   -0.054      0.076    0.065   \n",
              "beta[1, af]        -0.186  0.012  -0.209   -0.171      0.008    0.006   \n",
              "beta[1, pr]        -0.125  0.341  -0.477    0.219      0.240    0.203   \n",
              "beta[1, gn]        -0.173  0.075  -0.262   -0.092      0.053    0.045   \n",
              "beta[1, fb]        -0.184  0.011  -0.207   -0.170      0.007    0.006   \n",
              "mu_g[Delay, 0]      0.350  0.588  -0.271    0.949      0.414    0.350   \n",
              "mu_g[Delay, 1]      0.890  0.502   0.378    1.408      0.354    0.299   \n",
              "mu_g[HighPT, 0]     0.597  0.568   0.019    1.216      0.400    0.338   \n",
              "mu_g[HighPT, 1]     0.050  0.117  -0.088    0.186      0.082    0.069   \n",
              "mu_g[Imm, 0]        0.693  0.653   0.027    1.398      0.460    0.389   \n",
              "mu_g[Imm, 1]        0.043  0.203  -0.187    0.266      0.142    0.120   \n",
              "mu_g[LowPT, 0]     -0.187  0.195  -0.403    0.057      0.137    0.116   \n",
              "mu_g[LowPT, 1]     -0.175  0.804  -1.000    0.638      0.566    0.479   \n",
              "mu_g[NoBoth25, 0]  -0.571  1.176  -1.801    0.627      0.828    0.700   \n",
              "mu_g[NoBoth25, 1]   0.755  0.483   0.236    1.260      0.340    0.287   \n",
              "mu_g[NoBoth75, 0]  -0.574  1.123  -1.746    0.573      0.790    0.669   \n",
              "mu_g[NoBoth75, 1]   0.706  0.521   0.150    1.252      0.367    0.310   \n",
              "mu_g[NoRecal25, 0]  0.310  0.686  -0.413    1.005      0.482    0.408   \n",
              "mu_g[NoRecal25, 1]  0.947  0.506   0.432    1.470      0.356    0.301   \n",
              "mu_g[NoRecal75, 0]  0.290  0.637  -0.382    0.938      0.448    0.379   \n",
              "mu_g[NoRecal75, 1]  0.890  0.445   0.436    1.351      0.313    0.265   \n",
              "mu_g[NoStrat25, 0] -0.255  0.152  -0.429   -0.047      0.107    0.090   \n",
              "mu_g[NoStrat25, 1] -0.185  0.876  -1.083    0.701      0.617    0.522   \n",
              "mu_g[NoStrat75, 0] -0.230  0.137  -0.390   -0.045      0.096    0.081   \n",
              "mu_g[NoStrat75, 1] -0.154  0.828  -1.004    0.684      0.583    0.493   \n",
              "sigma_y             0.010  0.000   0.010    0.010      0.000    0.000   \n",
              "\n",
              "                    ess_bulk  ess_tail  r_hat  \n",
              "beta_0[lr]               2.0      11.0   2.38  \n",
              "beta_0[la]               2.0      11.0   2.87  \n",
              "beta_0[af]               2.0      11.0   2.93  \n",
              "beta_0[pr]               2.0      11.0   2.36  \n",
              "beta_0[gn]               2.0      11.0   2.93  \n",
              "beta_0[fb]               2.0      11.0   2.93  \n",
              "beta[0, lr]              2.0      12.0   2.49  \n",
              "beta[0, la]              2.0      11.0   2.63  \n",
              "beta[0, af]              3.0      12.0   2.24  \n",
              "beta[0, pr]              2.0      12.0   2.40  \n",
              "beta[0, gn]              2.0      11.0   2.46  \n",
              "beta[0, fb]              3.0      12.0   2.23  \n",
              "beta[1, lr]              3.0      11.0   2.16  \n",
              "beta[1, la]              2.0      11.0   2.60  \n",
              "beta[1, af]              3.0      11.0   2.31  \n",
              "beta[1, pr]              3.0      11.0   2.09  \n",
              "beta[1, gn]              2.0      11.0   2.61  \n",
              "beta[1, fb]              3.0      11.0   2.22  \n",
              "mu_g[Delay, 0]           3.0      15.0   1.85  \n",
              "mu_g[Delay, 1]           3.0      32.0   2.00  \n",
              "mu_g[HighPT, 0]          2.0      15.0   2.65  \n",
              "mu_g[HighPT, 1]          3.0      14.0   2.24  \n",
              "mu_g[Imm, 0]             2.0      19.0   2.77  \n",
              "mu_g[Imm, 1]             3.0      12.0   2.23  \n",
              "mu_g[LowPT, 0]           2.0      11.0   2.51  \n",
              "mu_g[LowPT, 1]           3.0      26.0   2.23  \n",
              "mu_g[NoBoth25, 0]        3.0      18.0   2.14  \n",
              "mu_g[NoBoth25, 1]        3.0      11.0   2.15  \n",
              "mu_g[NoBoth75, 0]        3.0      16.0   2.11  \n",
              "mu_g[NoBoth75, 1]        3.0      12.0   2.14  \n",
              "mu_g[NoRecal25, 0]       3.0      21.0   1.84  \n",
              "mu_g[NoRecal25, 1]       3.0      20.0   2.01  \n",
              "mu_g[NoRecal75, 0]       3.0      14.0   1.85  \n",
              "mu_g[NoRecal75, 1]       3.0      19.0   2.05  \n",
              "mu_g[NoStrat25, 0]       2.0      11.0   2.52  \n",
              "mu_g[NoStrat25, 1]       3.0      20.0   2.11  \n",
              "mu_g[NoStrat75, 0]       2.0      11.0   2.52  \n",
              "mu_g[NoStrat75, 1]       3.0      20.0   2.10  \n",
              "sigma_y                 79.0     582.0   1.01  "
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-1031b7e7-d914-45cf-80f6-33c9bb1bfde8\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>mean</th>\n",
              "      <th>sd</th>\n",
              "      <th>hdi_3%</th>\n",
              "      <th>hdi_97%</th>\n",
              "      <th>mcse_mean</th>\n",
              "      <th>mcse_sd</th>\n",
              "      <th>ess_bulk</th>\n",
              "      <th>ess_tail</th>\n",
              "      <th>r_hat</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>beta_0[lr]</th>\n",
              "      <td>0.864</td>\n",
              "      <td>0.091</td>\n",
              "      <td>0.766</td>\n",
              "      <td>0.966</td>\n",
              "      <td>0.064</td>\n",
              "      <td>0.054</td>\n",
              "      <td>2.0</td>\n",
              "      <td>11.0</td>\n",
              "      <td>2.38</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>beta_0[la]</th>\n",
              "      <td>0.900</td>\n",
              "      <td>0.081</td>\n",
              "      <td>0.814</td>\n",
              "      <td>0.988</td>\n",
              "      <td>0.057</td>\n",
              "      <td>0.048</td>\n",
              "      <td>2.0</td>\n",
              "      <td>11.0</td>\n",
              "      <td>2.87</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>beta_0[af]</th>\n",
              "      <td>0.919</td>\n",
              "      <td>0.076</td>\n",
              "      <td>0.838</td>\n",
              "      <td>1.001</td>\n",
              "      <td>0.053</td>\n",
              "      <td>0.045</td>\n",
              "      <td>2.0</td>\n",
              "      <td>11.0</td>\n",
              "      <td>2.93</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>beta_0[pr]</th>\n",
              "      <td>0.858</td>\n",
              "      <td>0.093</td>\n",
              "      <td>0.757</td>\n",
              "      <td>0.962</td>\n",
              "      <td>0.066</td>\n",
              "      <td>0.055</td>\n",
              "      <td>2.0</td>\n",
              "      <td>11.0</td>\n",
              "      <td>2.36</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>beta_0[gn]</th>\n",
              "      <td>0.906</td>\n",
              "      <td>0.079</td>\n",
              "      <td>0.823</td>\n",
              "      <td>0.992</td>\n",
              "      <td>0.055</td>\n",
              "      <td>0.047</td>\n",
              "      <td>2.0</td>\n",
              "      <td>11.0</td>\n",
              "      <td>2.93</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>beta_0[fb]</th>\n",
              "      <td>0.918</td>\n",
              "      <td>0.075</td>\n",
              "      <td>0.838</td>\n",
              "      <td>1.000</td>\n",
              "      <td>0.053</td>\n",
              "      <td>0.045</td>\n",
              "      <td>2.0</td>\n",
              "      <td>11.0</td>\n",
              "      <td>2.93</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>beta[0, lr]</th>\n",
              "      <td>0.186</td>\n",
              "      <td>0.025</td>\n",
              "      <td>0.155</td>\n",
              "      <td>0.216</td>\n",
              "      <td>0.017</td>\n",
              "      <td>0.015</td>\n",
              "      <td>2.0</td>\n",
              "      <td>12.0</td>\n",
              "      <td>2.49</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>beta[0, la]</th>\n",
              "      <td>-0.014</td>\n",
              "      <td>0.171</td>\n",
              "      <td>-0.188</td>\n",
              "      <td>0.166</td>\n",
              "      <td>0.120</td>\n",
              "      <td>0.102</td>\n",
              "      <td>2.0</td>\n",
              "      <td>11.0</td>\n",
              "      <td>2.63</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>beta[0, af]</th>\n",
              "      <td>-0.113</td>\n",
              "      <td>0.269</td>\n",
              "      <td>-0.385</td>\n",
              "      <td>0.163</td>\n",
              "      <td>0.190</td>\n",
              "      <td>0.160</td>\n",
              "      <td>3.0</td>\n",
              "      <td>12.0</td>\n",
              "      <td>2.24</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>beta[0, pr]</th>\n",
              "      <td>0.218</td>\n",
              "      <td>0.056</td>\n",
              "      <td>0.155</td>\n",
              "      <td>0.279</td>\n",
              "      <td>0.039</td>\n",
              "      <td>0.033</td>\n",
              "      <td>2.0</td>\n",
              "      <td>12.0</td>\n",
              "      <td>2.40</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>beta[0, gn]</th>\n",
              "      <td>-0.046</td>\n",
              "      <td>0.203</td>\n",
              "      <td>-0.253</td>\n",
              "      <td>0.164</td>\n",
              "      <td>0.143</td>\n",
              "      <td>0.121</td>\n",
              "      <td>2.0</td>\n",
              "      <td>11.0</td>\n",
              "      <td>2.46</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>beta[0, fb]</th>\n",
              "      <td>-0.113</td>\n",
              "      <td>0.268</td>\n",
              "      <td>-0.384</td>\n",
              "      <td>0.161</td>\n",
              "      <td>0.189</td>\n",
              "      <td>0.160</td>\n",
              "      <td>3.0</td>\n",
              "      <td>12.0</td>\n",
              "      <td>2.23</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>beta[1, lr]</th>\n",
              "      <td>-0.130</td>\n",
              "      <td>0.308</td>\n",
              "      <td>-0.451</td>\n",
              "      <td>0.181</td>\n",
              "      <td>0.217</td>\n",
              "      <td>0.184</td>\n",
              "      <td>3.0</td>\n",
              "      <td>11.0</td>\n",
              "      <td>2.16</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>beta[1, la]</th>\n",
              "      <td>-0.167</td>\n",
              "      <td>0.108</td>\n",
              "      <td>-0.289</td>\n",
              "      <td>-0.054</td>\n",
              "      <td>0.076</td>\n",
              "      <td>0.065</td>\n",
              "      <td>2.0</td>\n",
              "      <td>11.0</td>\n",
              "      <td>2.60</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>beta[1, af]</th>\n",
              "      <td>-0.186</td>\n",
              "      <td>0.012</td>\n",
              "      <td>-0.209</td>\n",
              "      <td>-0.171</td>\n",
              "      <td>0.008</td>\n",
              "      <td>0.006</td>\n",
              "      <td>3.0</td>\n",
              "      <td>11.0</td>\n",
              "      <td>2.31</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>beta[1, pr]</th>\n",
              "      <td>-0.125</td>\n",
              "      <td>0.341</td>\n",
              "      <td>-0.477</td>\n",
              "      <td>0.219</td>\n",
              "      <td>0.240</td>\n",
              "      <td>0.203</td>\n",
              "      <td>3.0</td>\n",
              "      <td>11.0</td>\n",
              "      <td>2.09</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>beta[1, gn]</th>\n",
              "      <td>-0.173</td>\n",
              "      <td>0.075</td>\n",
              "      <td>-0.262</td>\n",
              "      <td>-0.092</td>\n",
              "      <td>0.053</td>\n",
              "      <td>0.045</td>\n",
              "      <td>2.0</td>\n",
              "      <td>11.0</td>\n",
              "      <td>2.61</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>beta[1, fb]</th>\n",
              "      <td>-0.184</td>\n",
              "      <td>0.011</td>\n",
              "      <td>-0.207</td>\n",
              "      <td>-0.170</td>\n",
              "      <td>0.007</td>\n",
              "      <td>0.006</td>\n",
              "      <td>3.0</td>\n",
              "      <td>11.0</td>\n",
              "      <td>2.22</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mu_g[Delay, 0]</th>\n",
              "      <td>0.350</td>\n",
              "      <td>0.588</td>\n",
              "      <td>-0.271</td>\n",
              "      <td>0.949</td>\n",
              "      <td>0.414</td>\n",
              "      <td>0.350</td>\n",
              "      <td>3.0</td>\n",
              "      <td>15.0</td>\n",
              "      <td>1.85</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mu_g[Delay, 1]</th>\n",
              "      <td>0.890</td>\n",
              "      <td>0.502</td>\n",
              "      <td>0.378</td>\n",
              "      <td>1.408</td>\n",
              "      <td>0.354</td>\n",
              "      <td>0.299</td>\n",
              "      <td>3.0</td>\n",
              "      <td>32.0</td>\n",
              "      <td>2.00</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mu_g[HighPT, 0]</th>\n",
              "      <td>0.597</td>\n",
              "      <td>0.568</td>\n",
              "      <td>0.019</td>\n",
              "      <td>1.216</td>\n",
              "      <td>0.400</td>\n",
              "      <td>0.338</td>\n",
              "      <td>2.0</td>\n",
              "      <td>15.0</td>\n",
              "      <td>2.65</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mu_g[HighPT, 1]</th>\n",
              "      <td>0.050</td>\n",
              "      <td>0.117</td>\n",
              "      <td>-0.088</td>\n",
              "      <td>0.186</td>\n",
              "      <td>0.082</td>\n",
              "      <td>0.069</td>\n",
              "      <td>3.0</td>\n",
              "      <td>14.0</td>\n",
              "      <td>2.24</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mu_g[Imm, 0]</th>\n",
              "      <td>0.693</td>\n",
              "      <td>0.653</td>\n",
              "      <td>0.027</td>\n",
              "      <td>1.398</td>\n",
              "      <td>0.460</td>\n",
              "      <td>0.389</td>\n",
              "      <td>2.0</td>\n",
              "      <td>19.0</td>\n",
              "      <td>2.77</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mu_g[Imm, 1]</th>\n",
              "      <td>0.043</td>\n",
              "      <td>0.203</td>\n",
              "      <td>-0.187</td>\n",
              "      <td>0.266</td>\n",
              "      <td>0.142</td>\n",
              "      <td>0.120</td>\n",
              "      <td>3.0</td>\n",
              "      <td>12.0</td>\n",
              "      <td>2.23</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mu_g[LowPT, 0]</th>\n",
              "      <td>-0.187</td>\n",
              "      <td>0.195</td>\n",
              "      <td>-0.403</td>\n",
              "      <td>0.057</td>\n",
              "      <td>0.137</td>\n",
              "      <td>0.116</td>\n",
              "      <td>2.0</td>\n",
              "      <td>11.0</td>\n",
              "      <td>2.51</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mu_g[LowPT, 1]</th>\n",
              "      <td>-0.175</td>\n",
              "      <td>0.804</td>\n",
              "      <td>-1.000</td>\n",
              "      <td>0.638</td>\n",
              "      <td>0.566</td>\n",
              "      <td>0.479</td>\n",
              "      <td>3.0</td>\n",
              "      <td>26.0</td>\n",
              "      <td>2.23</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mu_g[NoBoth25, 0]</th>\n",
              "      <td>-0.571</td>\n",
              "      <td>1.176</td>\n",
              "      <td>-1.801</td>\n",
              "      <td>0.627</td>\n",
              "      <td>0.828</td>\n",
              "      <td>0.700</td>\n",
              "      <td>3.0</td>\n",
              "      <td>18.0</td>\n",
              "      <td>2.14</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mu_g[NoBoth25, 1]</th>\n",
              "      <td>0.755</td>\n",
              "      <td>0.483</td>\n",
              "      <td>0.236</td>\n",
              "      <td>1.260</td>\n",
              "      <td>0.340</td>\n",
              "      <td>0.287</td>\n",
              "      <td>3.0</td>\n",
              "      <td>11.0</td>\n",
              "      <td>2.15</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mu_g[NoBoth75, 0]</th>\n",
              "      <td>-0.574</td>\n",
              "      <td>1.123</td>\n",
              "      <td>-1.746</td>\n",
              "      <td>0.573</td>\n",
              "      <td>0.790</td>\n",
              "      <td>0.669</td>\n",
              "      <td>3.0</td>\n",
              "      <td>16.0</td>\n",
              "      <td>2.11</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mu_g[NoBoth75, 1]</th>\n",
              "      <td>0.706</td>\n",
              "      <td>0.521</td>\n",
              "      <td>0.150</td>\n",
              "      <td>1.252</td>\n",
              "      <td>0.367</td>\n",
              "      <td>0.310</td>\n",
              "      <td>3.0</td>\n",
              "      <td>12.0</td>\n",
              "      <td>2.14</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mu_g[NoRecal25, 0]</th>\n",
              "      <td>0.310</td>\n",
              "      <td>0.686</td>\n",
              "      <td>-0.413</td>\n",
              "      <td>1.005</td>\n",
              "      <td>0.482</td>\n",
              "      <td>0.408</td>\n",
              "      <td>3.0</td>\n",
              "      <td>21.0</td>\n",
              "      <td>1.84</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mu_g[NoRecal25, 1]</th>\n",
              "      <td>0.947</td>\n",
              "      <td>0.506</td>\n",
              "      <td>0.432</td>\n",
              "      <td>1.470</td>\n",
              "      <td>0.356</td>\n",
              "      <td>0.301</td>\n",
              "      <td>3.0</td>\n",
              "      <td>20.0</td>\n",
              "      <td>2.01</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mu_g[NoRecal75, 0]</th>\n",
              "      <td>0.290</td>\n",
              "      <td>0.637</td>\n",
              "      <td>-0.382</td>\n",
              "      <td>0.938</td>\n",
              "      <td>0.448</td>\n",
              "      <td>0.379</td>\n",
              "      <td>3.0</td>\n",
              "      <td>14.0</td>\n",
              "      <td>1.85</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mu_g[NoRecal75, 1]</th>\n",
              "      <td>0.890</td>\n",
              "      <td>0.445</td>\n",
              "      <td>0.436</td>\n",
              "      <td>1.351</td>\n",
              "      <td>0.313</td>\n",
              "      <td>0.265</td>\n",
              "      <td>3.0</td>\n",
              "      <td>19.0</td>\n",
              "      <td>2.05</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mu_g[NoStrat25, 0]</th>\n",
              "      <td>-0.255</td>\n",
              "      <td>0.152</td>\n",
              "      <td>-0.429</td>\n",
              "      <td>-0.047</td>\n",
              "      <td>0.107</td>\n",
              "      <td>0.090</td>\n",
              "      <td>2.0</td>\n",
              "      <td>11.0</td>\n",
              "      <td>2.52</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mu_g[NoStrat25, 1]</th>\n",
              "      <td>-0.185</td>\n",
              "      <td>0.876</td>\n",
              "      <td>-1.083</td>\n",
              "      <td>0.701</td>\n",
              "      <td>0.617</td>\n",
              "      <td>0.522</td>\n",
              "      <td>3.0</td>\n",
              "      <td>20.0</td>\n",
              "      <td>2.11</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mu_g[NoStrat75, 0]</th>\n",
              "      <td>-0.230</td>\n",
              "      <td>0.137</td>\n",
              "      <td>-0.390</td>\n",
              "      <td>-0.045</td>\n",
              "      <td>0.096</td>\n",
              "      <td>0.081</td>\n",
              "      <td>2.0</td>\n",
              "      <td>11.0</td>\n",
              "      <td>2.52</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mu_g[NoStrat75, 1]</th>\n",
              "      <td>-0.154</td>\n",
              "      <td>0.828</td>\n",
              "      <td>-1.004</td>\n",
              "      <td>0.684</td>\n",
              "      <td>0.583</td>\n",
              "      <td>0.493</td>\n",
              "      <td>3.0</td>\n",
              "      <td>20.0</td>\n",
              "      <td>2.10</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sigma_y</th>\n",
              "      <td>0.010</td>\n",
              "      <td>0.000</td>\n",
              "      <td>0.010</td>\n",
              "      <td>0.010</td>\n",
              "      <td>0.000</td>\n",
              "      <td>0.000</td>\n",
              "      <td>79.0</td>\n",
              "      <td>582.0</td>\n",
              "      <td>1.01</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-1031b7e7-d914-45cf-80f6-33c9bb1bfde8')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-1031b7e7-d914-45cf-80f6-33c9bb1bfde8 button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-1031b7e7-d914-45cf-80f6-33c9bb1bfde8');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 35
        }
      ],
      "source": [
        "post = fit.posterior\n",
        "obs = fit.observed_data\n",
        "post['y_err'] = obs.obs_y - post.mu_y\n",
        "\n",
        "az.summary(fit, ['beta_0', 'beta', 'mu_g', 'sigma_y'])\n",
        "\n"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "collapsed_sections": [],
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "display_name": "Python 3 (ipykernel)",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.10.6"
    },
    "vscode": {
      "interpreter": {
        "hash": "71f527b1031338ab6b141ba7e1c274cf8d73937106b79c3402044bb2b293c7ce"
      }
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}