notes/Inverse-Transform-Sampling.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import random\n",
    "from scipy.stats import norm,uniform"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Inverse transform sampling** is a basic method for pseudo-random number sampling, i.e. for generating sample numbers at random from any probability distribution given its cumulative distribution function. It works as follows,\n",
    "1. Generate a random number $u$ from the standard uniform distribution in the interval $[0,1]$.\n",
    "$$U\\sim \\mathbb{U}[0,1]$$\n",
    "2. Find the inverse of the desired CDF. \n",
    "$$F_X^{-1}(x)$$\n",
    "3. Computer $X=F^{-1}_X(u)$. The computed random variable $X$ has distribution $F_X(x)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "CDF is always an increasing function, it represents the probability that $X$ will take a value less than or equal to $x$, and is defined as $F_X(x)$. If there is a transformation such that it turns probability to $X$, i.e. $T:[0,1]\\rightarrow \\mathbb{R}$, so that $T(U)=^d X$ and $U\\sim \\mathbb{U}[0,1]$.\n",
    "\n",
    "$$F_X(x) = P(X\\leq x)=P(T(U)\\leq x) = P(U\\leq T^{-1}(x))=T^{-1}(x)$$\n",
    "\n",
    "Inverse CDF is the probability that $U$ will take a value less than or equal to $F_X(x)=y$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "lamb,N = 1,1000\n",
    "X = np.linspace(0,10,N)\n",
    "f = lambda x: np.exp(-x/lamb)/lamb\n",
    "F = lambda x: (1-np.exp(-x/lamb))\n",
    "invF = lambda p: -lamb*np.log(1-p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f0e3c61d250>]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X,f(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f0e3c531fd0>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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hVxv2E8kxbrtodtCliIikRGf6hhGLOU+81sQ7a2boMbkikjEU6MN4+Y029h/p5c803CIiGUSBPoxfb9jP5PwINy2dFXQpIiIpU6AP0T8Y46nNB/hPy2YxKV9zhopI5lCgD/Hi7kN09g3y7gvPCboUEZEzokAf4qlNBygpyOUdNTOCLkVE5Iwo0JMMRGP8ZutBblhaQUGuhltEJLMo0JP8cfdhjvQMcOsFGm4RkcyjQE+y+vUDFBfk8k4Nt4hIBlKgJwxEYzyztZkV582kME/DLSKSeRToCWv3aLhFRDKbAj3h6c3NFOVHuHbxxH9Ou4jIcBTogLuzZlsL19SUa7hFRDKWAh3Y0tRJc2cfK84LzdzWIpKFFOjAb7cexAyuX6JAF5HMpUAH1mw/yMVzp1NWrEflikjmyvpAP9DRy+b9ndxwXkXQpYiInJWsD/Q121oAuEHj5yKS4bI+0H+37SDzyopYNLM46FJERM5KVgf60WOD/HH3YVYsqcDMgi5HROSsZHWgv1h/iP7BmIZbRCQUsjrQX9jVSlF+hNrq0qBLERE5a9kd6DsPceWCMvJzs/o/g4iERNYm2ZuHj7KvrYdr9OwWEQmJrA30F3a2AijQRSQ0sjbQn995iKrSSVSXFQVdiohIWmRloPcPxnhp9yGuqSnX5YoiEhpZGegb9rVztD/KO2s03CIi4ZGVgf7CrlYiOcZVi8qCLkVEJG2yM9B3HuLiudOYUpgXdCkiImmTdYHefrSfzU0dGm4RkdBJKdDN7GYz22Fm9WZ2/9v0e5+ZuZnVpq/E9Hr5jTbc4aqFGm4RkXAZMdDNLAI8BNwCLAXuNLOlw/QrAT4DvJzuItNp7Z7DTMqLcGHltKBLERFJq1SO0C8D6t19j7v3A48Ctw/T78vA14C+NNaXdi/tPkxt9XTd7i8ioZNKqs0BGpLWGxNtJ5jZcqDK3Z98ux2Z2T1mVmdmda2trWdc7Nk63H2MHQe7uGKBhltEJHxSCfTh7rzxExvNcoBvAveNtCN3f9jda929trx8/E9KvvxGG4ACXURCKZVAbwSqktYrgaak9RLgfOA5M9sLXAGsmognRl/afZii/AgXVk4NuhQRkbRLJdDXATVmNt/M8oE7gFXHN7p7h7vPcPdqd68G1gK3uXvdmFR8FtbuOcyl1aXkRTR+LiLhM2KyufsgcC/wDLANWOnuW8zsQTO7bawLTJfWrmPsaunWcIuIhFZuKp3cfTWwekjbA6fpe93Zl5V+a/ccBuBKXX8uIiGVNWMPa/ccprggl/NnTwm6FBGRMZE1gf7KG23UVk8nV+PnIhJSWZFuR3r62dXSzaWaDFpEQiwrAn39m+0AXDJvesCViIiMnawI9Lo328nNMS7S81tEJMSyItDX721n2ZypTMqPBF2KiMiYCX2g9w/G2Nh4hFoNt4hIyIU+0Dc3dXBsMKZAF5HQC32gr9+bOCFarUAXkXALfaDXvdnGvLIiZpYUBl2KiMiYCnWguzt1e9t1uaKIZIVQB/rewz0cPtpP7TzdUCQi4RfqQK/bG5/Qolbj5yKSBUId6BsajlBSmMui8uKgSxERGXOhDvSNDUe4qHIaOTnDzaInIhIuoQ30voEo25u7uKhK082JSHYIbaBvaeogGnM9v0VEskZoA31jQwcAf1KlQBeR7BDeQG88wjlTC5k5RTcUiUh2CG+gJ06Iiohki1AG+pGefvYe7uEiDbeISBYJZaBvbIyPn+sKFxHJJuEM9IYjmMEFcxToIpI9Qhvoi8qLKSnMC7oUEZFxE7pAd3c2Nh7R+LmIZJ3QBfr+I70c6u5XoItI1gldoG9KnBC9UOPnIpJlQhfoW5o6ieQY584qCboUEZFxFbpA39zUQc3MYgrzIkGXIiIyrkIX6FuaOlk2W8MtIpJ9Ugp0M7vZzHaYWb2Z3T/M9s+b2VYze93M1pjZvPSXOrKWzj5au46xbPaUID5eRCRQIwa6mUWAh4BbgKXAnWa2dEi3DUCtu18IPAZ8Ld2FpmJLUyeAAl1EslIqR+iXAfXuvsfd+4FHgduTO7j77929J7G6FqhMb5mp2dIUv8JlqQJdRLJQKoE+B2hIWm9MtJ3O3cBTw20ws3vMrM7M6lpbW1OvMkWb93dSXVakO0RFJCulEujDTcjpw3Y0+whQC3x9uO3u/rC717p7bXl5eepVpmjLgQ6dEBWRrJVKoDcCVUnrlUDT0E5mdgPwP4Hb3P1YespLXUfPAA1tvSybo+EWEclOqQT6OqDGzOabWT5wB7AquYOZLQf+mXiYt6S/zJFtORAfP9cRuohkqxED3d0HgXuBZ4BtwEp332JmD5rZbYluXweKgV+Y2Wtmtuo0uxszW3WFi4hkudxUOrn7amD1kLYHkpZvSHNdZ2xLUyezphQyo7gg6FJERAIRmjtFN+/v0NG5iGS1UAR630CU3a3duv5cRLJaKAK9vqWbmMOSWQp0EcleoQj07c1dAHpkrohktVAE+o7mTvJzc6guKwq6FBGRwIQi0Lc3d7G4opjcSCi+jojIqIQiAXc0d3FuhcbPRSS7ZXygtx3tp6XrGEs0fi4iWS7jA317c/wOUZ0QFZFsl/GBviNxhYuO0EUk24Ui0KcX5VFeolv+RSS7ZXygb2/u4txZJZgN99h2EZHskdGBHos5Ow926Q5REREyPNAb23vp6Y9q/FxEhAwPdF3hIiLylowO9ONXuCyuUKCLiGR0oG8/2MXc0iImF6Q0T4eISKhldKDXH+xmcUVx0GWIiEwIGRvog9EYew51s3CmAl1EBDI40Pe19TAQdWpmavxcRAQyONDrW7oBWKQjdBERIJMDvTUe6AvLJwdciYjIxJC5gd7SzawphZQU5gVdiojIhJDRga7hFhGRt2RkoLs7uxXoIiInychAP9DRx9H+qAJdRCRJRga6rnARETlVRgb6LgW6iMgpMjLQ61u6mVaUR9nk/KBLERGZMDIy0He3dFMzs1izFImIJMnIQK9v1RUuIiJDpRToZnazme0ws3ozu3+Y7QVm9m+J7S+bWXW6Cz3ucPcx2o72s7BcgS4ikmzEQDezCPAQcAuwFLjTzJYO6XY30O7ui4BvAl9Nd6HH6QoXEZHhpXKEfhlQ7+573L0feBS4fUif24EfJ5YfA1bYGA1wH3+GiwJdRORkqQT6HKAhab0x0TZsH3cfBDqAsqE7MrN7zKzOzOpaW1tHVXB5cQE3Lq1g9tRJo3q/iEhYpTJ323BH2j6KPrj7w8DDALW1tadsT8VNy2Zx07JZo3mriEiopXKE3ghUJa1XAk2n62NmucBUoC0dBYqISGpSCfR1QI2ZzTezfOAOYNWQPquAuxLL7wOedfdRHYGLiMjojDjk4u6DZnYv8AwQAX7g7lvM7EGgzt1XAf8X+KmZ1RM/Mr9jLIsWEZFTpTKGjruvBlYPaXsgabkPeH96SxMRkTORkXeKiojIqRToIiIhoUAXEQkJBbqISEhYUFcXmlkr8OYo3z4DOJTGcjKBvnN20HfODmfznee5e/lwGwIL9LNhZnXuXht0HeNJ3zk76Dtnh7H6zhpyEREJCQW6iEhIZGqgPxx0AQHQd84O+s7ZYUy+c0aOoYuIyKky9QhdRESGUKCLiIRExgX6SBNWh42ZVZnZ781sm5ltMbPPBl3TeDCziJltMLMng65lPJjZNDN7zMy2J/6srwy6prFmZp9L/E5vNrNHzKww6JrSzcx+YGYtZrY5qa3UzH5rZrsSr9PT9XkZFegpTlgdNoPAfe5+HnAF8Kks+M4AnwW2BV3EOPoW8LS7LwEuIuTf3czmAJ8Bat39fOKP5g7jY7d/BNw8pO1+YI271wBrEutpkVGBTmoTVoeKux9w91cTy13E/6IPndM1VMysEng38P2gaxkPZjYFuIb4vAK4e7+7Hwm2qnGRC0xKzHJWxKkzoWU8d3+BU2dvux34cWL5x8B70vV5mRboqUxYHVpmVg0sB14OtpIx94/AXwGxoAsZJwuAVuCHiWGm75vZ5KCLGkvuvh/4BrAPOAB0uPtvgq1q3FS4+wGIH7ABM9O140wL9JQmow4jMysGfgn8N3fvDLqesWJm/xlocff1QdcyjnKBi4Hvuvty4Chp/Gf4RJQYN74dmA/MBiab2UeCrSrzZVqgpzJhdeiYWR7xMP+Zuz8edD1j7GrgNjPbS3xI7Xoz+9dgSxpzjUCjux//l9djxAM+zG4A3nD3VncfAB4Hrgq4pvFy0MzOAUi8tqRrx5kW6KlMWB0qZmbEx1a3ufs/BF3PWHP3L7h7pbtXE//zfdbdQ33k5u7NQIOZnZtoWgFsDbCk8bAPuMLMihK/4ysI+YngJKuAuxLLdwFPpGvHKc0pOlGcbsLqgMsaa1cDHwU2mdlribYvJuZ5lfD4NPCzxIHKHuBjAdczptz9ZTN7DHiV+JVcGwjhIwDM7BHgOmCGmTUCfw38PbDSzO4m/j+2tM3HrFv/RURCItOGXERE5DQU6CIiIaFAFxEJCQW6iEhIKNBFREJCgS4iEhIKdBGRkPj/VwXo1tlDvFkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X,F(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/yui/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:5: RuntimeWarning: divide by zero encountered in log\n",
      "  \"\"\"\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f0e3c523f90>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = np.linspace(0,1,N)\n",
    "plt.plot(p,invF(p))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "U = uniform.rvs(0,1,N)\n",
    "_ = plt.hist(U,bins=50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = plt.hist(invF(U),bins=50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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