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@article{Cowles2004,
doi = {10.1198/000313004x8515},
url = {https://doi.org/10.1198/000313004x8515},
year = {2004},
month = {Nov},
publisher = {Informa UK Limited},
volume = {58},
number = {4},
pages = {330--336},
author = {Mary Kathryn Cowles},
title = {Review of WinBUGS 1.4},
journal = {The American Statistician}
}
@article{Salvatier2016,
doi = {10.7717/peerj-cs.55},
url = {https://doi.org/10.7717/peerj-cs.55},
year = {2016},
month = {apr},
publisher = {PeerJ},
volume = {2},
pages = {e55},
author = {John Salvatier and Thomas V. Wiecki and Christopher Fonnesbeck},
title = {Probabilistic programming in Python using PyMC3},
journal = {PeerJ Computer Science}
}
@book{jaynes2003,
place = {Cambridge},
title = {Probability Theory: The Logic of Science},
DOI = {10.1017/CBO9780511790423},
publisher = {Cambridge University Press},
author = {Jaynes, E. T.},
editor = {Bretthorst, G. LarryEditor},
year = {2003}
}
@book{BMCP2021,
title = {{Bayesian Modeling and Computation in Python}},
author = {Martin, Osvaldo A. and Kumar, Ravin and Lao, Junpeng},
year = {2021},
address = {{Boca Raton, FL}},
isbn = {978-0-367-89436-8},
}
@book{mcelreath2020statistical,
title = {Statistical Rethinking: A Bayesian Course with Examples in R and Stan},
author = {McElreath, Richard},
year = {2020},
edition = {2nd},
publisher = {CRC Press},
address = {Boca Raton, FL},
isbn = {978-0367139919}
}
@book{gelman2013bayesian,
title = {Bayesian Data Analysis},
author = {Gelman, Andrew and Carlin, John B. and Stern, Hal S. and Dunson, David B. and Vehtari, Aki and Rubin, Donald B.},
year = {2013},
edition = {3rd},
publisher = {CRC Press},
address = {Boca Raton, FL},
isbn = {978-1439840955}
}
@book{pml1Book,
author = "Kevin P. Murphy",
title = "Probabilistic Machine Learning: An introduction",
publisher = "MIT Press",
year = {2022},
url = "probml.ai"
}
@book{robert2007bayesian,
title = {The Bayesian Choice},
subtitle = {From Decision-Theoretic Foundations to Computational Implementation},
author = {Robert, Christian P.},
year = {2007},
edition = {2nd},
publisher = {Springer},
address = {New York, NY},
isbn = {978-0-387-71598-8},
doi = {10.1007/0-387-71599-1},
series = {Springer Texts in Statistics},
note = {Hardcover ISBN: 978-0-387-95231-4, Published: 25 May 2001; Softcover ISBN: 978-0-387-71598-8, Published: 27 August 2007; eBook ISBN: 978-0-387-71599-5, Published: 19 May 2007},
ebookpackages = {Mathematics and Statistics, Mathematics and Statistics (R0)},
issn = {1431-875X},
eissn = {2197-4136},
pages = {XXIV, 606},
topics = {Probability Theory, Statistical Theory and Methods}
}
@book{vidakovic2017engineering,
title={Engineering Biostatistics: An Introduction using MATLAB and WinBUGS},
author={Vidakovic, Brani},
year={2017},
publisher={Wiley},
isbn={978-1-119-16896-6}
}
@article{chen1999monte,
title = {Monte Carlo Estimation of Bayesian Credible and {HPD} Intervals},
author = {Chen, Ming-Hui and Shao, Qi-Man},
journal = {Journal of Computational and Graphical Statistics},
volume = {8},
number = {1},
year = {1999},
pages = {69--92},
doi = {10.2307/1390921},
url = {https://doi.org/10.2307/1390921},
}
@book{jeffreystheoryofprob,
title = {Theory of probability, 3rd Edition},
author = {Harold Jeffreys},
publisher = {Clarendon Press},
isbn = {0198503687; 9780198503682},
year = {2003},
series = {Oxford Classic Texts in the Physical Sciences},
edition = {3},
}
@book{lee2013bayesian,
title={Bayesian Cognitive Modeling: A Practical Course},
author={Lee, Michael D and Wagenmakers, Eric J.},
year={2013},
publisher={Cambridge University Press}
}
@article{kass1995bayes,
title={Bayes factors},
author={Kass, Robert E and Raftery, Adrian E},
journal={Journal of the American Statistical Association},
volume={90},
number={430},
pages={773--795},
year={1995},
publisher={Taylor \& Francis Group}
}
@article{elicitationgarthwaite,
author = {Garthwaite, Paul H. and Dickey, James M.},
title = {Quantifying Expert Opinion in Linear Regression Problems},
journal = {Journal of the Royal Statistical Society: Series B (Methodological)},
volume = {50},
number = {3},
pages = {462-474},
keywords = {bayesian regression analysis, elicitation tasks, normal linear model, prior assessment, prior distributions, probability assessment, probability elicitation},
doi = {https://doi.org/10.1111/j.2517-6161.1988.tb01741.x},
url = {https://rss.onlinelibrary.wiley.com/doi/abs/10.1111/j.2517-6161.1988.tb01741.x},
eprint = {https://rss.onlinelibrary.wiley.com/doi/pdf/10.1111/j.2517-6161.1988.tb01741.x},
abstract = {SUMMARY This paper describes a method for choosing a natural conjugate prior distribution for a normal linear sampling model. A person using the method to quantify his/her opinions performs specified elicitation tasks. The hyperparameters of the conjugate distribution are estimated from the elicited values. The method is designed to require elicitation tasks that people can perform competently and introduces a type of task not previously reported. A property of the method is that the assessed variance matrices are certain to be positive definite. The method is sufficiently simple to implement with an interactive computer program on a microcomputer.},
year = {1988}
}
@article{robbinsempirical,
ISSN = {00034851},
URL = {https://www.jstor.org/stable/2238017},
author = {Herbert Robbins},
journal = {The Annals of Mathematical Statistics},
number = {1},
pages = {1--20},
publisher = {Institute of Mathematical Statistics},
title = {The Empirical Bayes Approach to Statistical Decision Problems},
urldate = {2023-07-10},
volume = {35},
year = {1964}
}
@article{morrisempirical,
ISSN = {01621459},
URL = {http://www.jstor.org/stable/2287098},
abstract = {This article reviews the state of multiparameter shrinkage estimators with emphasis on the empirical Bayes viewpoint, particularly in the case of parametric prior distributions. Some successful applications of major importance are considered. Recent results concerning estimates of error and confidence intervals are described and illustrated with data.},
author = {Carl N. Morris},
journal = {Journal of the American Statistical Association},
number = {381},
pages = {47--55},
publisher = {[American Statistical Association, Taylor & Francis, Ltd.]},
title = {Parametric Empirical Bayes Inference: Theory and Applications},
urldate = {2023-07-10},
volume = {78},
year = {1983}
}
@article{kass1996selection,
title={The selection of prior distributions by formal rules},
author={Kass, Robert E and Wasserman, Larry},
journal={Journal of the American Statistical Association},
volume={91},
number={435},
pages={1343--1370},
year={1996},
publisher={Taylor & Francis}
}
@article{berger2006case,
title={The case for objective Bayesian analysis},
author={Berger, James O},
journal={Bayesian Analysis},
volume={1},
number={3},
pages={385--402},
year={2006},
publisher={International Society for Bayesian Analysis}
}
@article{gelman2017beyond,
title={Beyond subjective and objective in statistics},
author={Gelman, Andrew and Hennig, Christian},
journal={Journal of the Royal Statistical Society: Series A (Statistics in Society)},
volume={180},
number={4},
pages={967--1033},
year={2017},
publisher={Wiley Online Library}
}
@article{spiegelhalterpriors,
ISSN = {09641998, 1467985X},
URL = {http://www.jstor.org/stable/2983527},
abstract = {Statistical issues in conducting randomized trials include the choice of a sample size, whether to stop a trial early and the appropriate analysis and interpretation of the trial results. At each of these stages, evidence external to the trial is useful, but generally such evidence is introduced in an unstructured and informal manner. We argue that a Bayesian approach allows a formal basis for using external evidence and in addition provides a rational way for dealing with issues such as the ethics of randomization, trials to show treatment equivalence, the monitoring of accumulating data and the prediction of the consequences of continuing a study. The motivation for using this methodology is practical rather than ideological.},
author = {David J. Spiegelhalter and Laurence S. Freedman and Mahesh K. B. Parmar},
journal = {Journal of the Royal Statistical Society. Series A (Statistics in Society)},
number = {3},
pages = {357--416},
publisher = {[Wiley, Royal Statistical Society]},
title = {Bayesian Approaches to Randomized Trials},
urldate = {2023-07-10},
volume = {157},
year = {1994}
}
@article{Blei_2017,
doi = {10.1080/01621459.2017.1285773},
url = {https://doi.org/10.1080%2F01621459.2017.1285773},
year = 2017,
month = {apr},
publisher = {Informa {UK} Limited},
volume = {112},
number = {518},
pages = {859--877},
author = {David M. Blei and Alp Kucukelbir and Jon D. McAuliffe},
title = {Variational Inference: A Review for Statisticians},
journal = {Journal of the American Statistical Association}
}
@misc{mikkola2023prior,
title={Prior knowledge elicitation: The past, present, and future},
author={Petrus Mikkola and Osvaldo A. Martin and Suyog Chandramouli and Marcelo Hartmann and Oriol Abril Pla and Owen Thomas and Henri Pesonen and Jukka Corander and Aki Vehtari and Samuel Kaski and Paul-Christian Bürkner and Arto Klami},
year={2023},
eprint={2112.01380},
archivePrefix={arXiv},
primaryClass={stat.ME}
}
@article{metropolis1953,
title={Equation of State Calculations by Fast Computing Machines},
author={Metropolis, Nicholas and Rosenbluth, Arianna W. and Rosenbluth, Marshall N. and Teller, Augusta H. and Teller, Edward},
journal={The Journal of Chemical Physics},
volume={21},
number={6},
pages={1087--1092},
year={1953},
publisher={AIP}
}
@article{hastings1970,
ISSN = {00063444},
URL = {http://www.jstor.org/stable/2334940},
abstract = {A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.},
author = {W. K. Hastings},
journal = {Biometrika},
number = {1},
pages = {97--109},
publisher = {[Oxford University Press, Biometrika Trust]},
title = {Monte Carlo Sampling Methods Using Markov Chains and Their Applications},
urldate = {2023-07-16},
volume = {57},
year = {1970}
}
@ARTICLE{gehmanbros1984,
author={Geman, Stuart and Geman, Donald},
journal={IEEE Transactions on Pattern Analysis and Machine Intelligence},
title={Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images},
year={1984},
volume={PAMI-6},
number={6},
pages={721-741},
doi={10.1109/TPAMI.1984.4767596}}
@article{DUANE1987216,
title = {Hybrid Monte Carlo},
journal = {Physics Letters B},
volume = {195},
number = {2},
pages = {216-222},
year = {1987},
issn = {0370-2693},
doi = {https://doi.org/10.1016/0370-2693(87)91197-X},
url = {https://www.sciencedirect.com/science/article/pii/037026938791197X},
author = {Simon Duane and A.D. Kennedy and Brian J. Pendleton and Duncan Roweth},
abstract = {We present a new method for the numerical simulation of lattice field theory. A hybrid (molecular dynamics/Langevin) algorithm is used to guide a Monte Carlo simulation. There are no discretization errors even for large step sizes. The method is especially efficient for systems such as quantum chromodynamics which contain fermionic degrees of freedom. Detailed results are presented for four-dimensional compact quantum electrodynamics including the dynamical effects of electrons.}
}
@book{ntzoufras2009bayesian,
title={Bayesian Modeling Using WinBUGS},
author={Ntzoufras, Ioannis},
year={2009},
publisher={John Wiley \& Sons, Inc.},
address={Hoboken, New Jersey},
edition={1},
isbn={978-0-470-14114-4},
series={}
}
@article{karlisfootball,
author = {Karlis, Dimitris and Ntzoufras, Ioannis},
title = "{Bayesian modelling of football outcomes: using the Skellam's distribution for the goal difference}",
journal = {IMA Journal of Management Mathematics},
volume = {20},
number = {2},
pages = {133-145},
year = {2008},
month = {09},
abstract = "{Modelling football match outcomes is becoming increasingly popular nowadays for both team managers and betting funs. Most of the existing literature deals with modelling the number of goals scored by each team. In this paper, we work in a different direction. Instead of modelling the number of goals directly, we focus on the difference of the number of goals, i.e. the margin of victory. Modelling the differences instead of the scores themselves has some major advantages. Firstly, we eliminate correlation imposed by the fact that the two opponent teams compete each other, and secondly, we do not assume that the scored goals by each team are marginally Poisson distributed. Application of the Bayesian methodology for the Skellam's distribution using covariates is discussed. Illustrations using real data from the English Premiership for the season 2006–2007 are provided. The advantages of the proposed approach are also discussed.}",
issn = {1471-678X},
doi = {10.1093/imaman/dpn026},
url = {https://doi.org/10.1093/imaman/dpn026},
eprint = {https://academic.oup.com/imaman/article-pdf/20/2/133/2118878/dpn026.pdf}
}
@article{BUGSoriginal,
ISSN = {00390526, 14679884},
URL = {http://www.jstor.org/stable/2348941},
abstract = {Gibbs sampling has enormous potential for analysing complex data sets. However, routine use of Gibbs sampling has been hampered by the lack of general purpose software for its implementation. Until now all applications have involved writing one-off computer code in low or intermediate level languages such as C or Fortran. We describe some general purpose software that we are currently developing for implementing Gibbs sampling: BUGS (Bayesian inference using Gibbs sampling). The BUGS system comprises three components: first, a natural language for specifying complex models; second, an 'expert system' for deciding appropriate methods for obtaining samples required by the Gibbs sampler: third, a sampling module containing numerical routines to perform the sampling. $S$ objects are used for data input and output. BUGS is written in Modula-2 and runs under both DOS and UNIX.},
author = {W. R. Gilks and A. Thomas and D. J. Spiegelhalter},
journal = {Journal of the Royal Statistical Society. Series D (The Statistician)},
number = {1},
pages = {169--177},
publisher = {[Royal Statistical Society, Wiley]},
title = {A Language and Program for Complex Bayesian Modelling},
urldate = {2023-08-20},
volume = {43},
year = {1994}
}
@article{lunn2000winbugs,
title={WinBUGS -- A Bayesian modelling framework: Concepts, structure, and extensibility},
author={Lunn, D.J. and Thomas, A. and Best, N. and others},
journal={Statistics and Computing},
volume={10},
pages={325--337},
year={2000},
doi={10.1023/A:1008929526011}
}
@article{conjugatelikelihoods1993,
ISSN = {03036898, 14679469},
URL = {http://www.jstor.org/stable/4616270},
abstract = {Families of probability distributions which arise naturally as parameter likelihoods in conjugate prior distributions for exponential families are identified, described and their relevance to computational issues in Bayes hierarchical models noted.},
author = {E. I. George and U. E. Makov and A. F. M. Smith},
journal = {Scandinavian Journal of Statistics},
number = {2},
pages = {147--156},
publisher = {[Board of the Foundation of the Scandinavian Journal of Statistics, Wiley]},
title = {Conjugate Likelihood Distributions},
urldate = {2023-08-22},
volume = {20},
year = {1993}
}
@article{gaverpoisson,
ISSN = {00401706},
URL = {http://www.jstor.org/stable/1269878},
abstract = {A collection of I similar items generates point event histories; for example, machines experience failures or operators make mistakes. Suppose the intervals between events are modeled as iid exponential (λ i), or the counts as Poisson (λ iti), for the ith item. Furthermore, so as to represent between-item variability, each individual rate parameter λ i, is presumed drawn from a fixed (super) population with density gλ(·;θ), θ being a vector parameter: a parametric empirical Bayes (PEB) setup. For gλ, specified alternatively as long-Student t(n) or gamma, we exhibit the results of numerical procedures for estimating superpopulation parameters θ and for describing pooled estimates of the individual rates λ i, obtained via Bayes's formula. Three data sets are analyzed, and convenient explicit approximate formulas are furnished for λ i estimates. In the Student-t case, the individual estimates are seen to have a robust quality.},
author = {Donald P. Gaver and I. G. O'Muircheartaigh},
journal = {Technometrics},
number = {1},
pages = {1--15},
publisher = {[Taylor & Francis, Ltd., American Statistical Association, American Society for Quality]},
title = {Robust Empirical Bayes Analyses of Event Rates},
urldate = {2023-08-27},
volume = {29},
year = {1987}
}
@misc{betancourt2018conceptual,
title={A Conceptual Introduction to Hamiltonian Monte Carlo},
author={Michael Betancourt},
year={2018},
eprint={1701.02434},
archivePrefix={arXiv},
primaryClass={stat.ME}
}
@article{ukcoaldisasteroriginal,
author = {MAGUIRE, B. A. and PEARSON, E. S. and WYNN, A. H. A.},
title = "{THE TIME INTERVALS BETWEEN INDUSTRIAL ACCIDENTS}",
journal = {Biometrika},
volume = {39},
number = {1-2},
pages = {168-180},
year = {1952},
month = {05},
issn = {0006-3444},
doi = {10.1093/biomet/39.1-2.168},
url = {https://doi.org/10.1093/biomet/39.1-2.168},
eprint = {https://academic.oup.com/biomet/article-pdf/39/1-2/168/834479/39-1-2-168.pdf},
}
@article{ukcoaldisasterupdate,
ISSN = {00063444},
URL = {http://www.jstor.org/stable/2335266},
abstract = {Two graphical procedures for analysing distributions of survival time are compared. One works with the survivor function, or with the order statistics, and the other is based on estimates of log hazard and is designed to give points with independent errors of constant known variance.},
author = {R. G. Jarrett},
journal = {Biometrika},
number = {1},
pages = {191--193},
publisher = {[Oxford University Press, Biometrika Trust]},
title = {A Note on the Intervals Between Coal-Mining Disasters},
urldate = {2023-08-27},
volume = {66},
year = {1979}
}
@article{carlinchangepoint1992,
ISSN = {00359254, 14679876},
URL = {http://www.jstor.org/stable/2347570},
abstract = {A general approach to hierarchical Bayes changepoint models is presented. In particular, desired marginal posterior densities are obtained utilizing the Gibbs sampler, an iterative Monte Carlo method. This approach avoids sophisticated analytic and numerical high dimensional integration procedures. We include an application to changing regressions, changing Poisson processes and changing Markov chains. Within these contexts we handle several previously inaccessible problems.},
author = {Bradley P. Carlin and Alan E. Gelfand and Adrian F. M. Smith},
journal = {Journal of the Royal Statistical Society. Series C (Applied Statistics)},
number = {2},
pages = {389--405},
publisher = {[Wiley, Royal Statistical Society]},
title = {Hierarchical Bayesian Analysis of Changepoint Problems},
urldate = {2023-08-27},
volume = {41},
year = {1992}
}
@article{pymc_all_versions,
author = {Thomas Wiecki and
John Salvatier and
Ricardo Vieira and
Maxim Kochurov and
Anand Patil and
Michael Osthege and
Brandon T. Willard and
Bill Engels and
Colin Carroll and
Osvaldo A Martin and
Adrian Seyboldt and
Austin Rochford and
Luciano Paz and
rpgoldman and
Kyle Meyer and
Peadar Coyle and
Marco Edward Gorelli and
Oriol Abril-Pla and
Ravin Kumar and
Junpeng Lao and
Virgile Andreani and
Taku Yoshioka and
George Ho and
Thomas Kluyver and
Kyle Beauchamp and
Alexandre Andorra and
Demetri Pananos and
Eelke Spaak and
Benjamin Edwards and
Eric Ma},
journal = {},
title = {pymc-devs/pymc: v5.7.2},
month = {aug},
year = {2023},
publisher = {Zenodo},
version = {v5.7.2},
doi = {10.5281/zenodo.8227797},
url = {https://doi.org/10.5281/zenodo.8227797}
}
@misc{hoffman2011nouturn,
title={The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo},
author={Matthew D. Hoffman and Andrew Gelman},
year={2011},
eprint={1111.4246},
archivePrefix={arXiv},
primaryClass={stat.CO}
}
@article{gelmanstandardization,
author = {Gelman, Andrew},
title = {Scaling regression inputs by dividing by two standard deviations},
journal = {Statistics in Medicine},
volume = {27},
number = {15},
pages = {2865-2873},
keywords = {generalized linear models, linear regression, logistic regression, standardization, z-score},
doi = {https://doi.org/10.1002/sim.3107},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.3107},
eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/sim.3107},
abstract = {Abstract Interpretation of regression coefficients is sensitive to the scale of the inputs. One method often used to place input variables on a common scale is to divide each numeric variable by its standard deviation. Here we propose dividing each numeric variable by two times its standard deviation, so that the generic comparison is with inputs equal to the mean ±1 standard deviation. The resulting coefficients are then directly comparable for untransformed binary predictors. We have implemented the procedure as a function in R. We illustrate the method with two simple analyses that are typical of applied modeling: a linear regression of data from the National Election Study and a multilevel logistic regression of data on the prevalence of rodents in New York City apartments. We recommend our rescaling as a default option—an improvement upon the usual approach of including variables in whatever way they are coded in the data file—so that the magnitudes of coefficients can be directly compared as a matter of routine statistical practice. Copyright © 2007 John Wiley \& Sons, Ltd.},
year = {2008}
}
@article{arviz_2019,
doi = {10.21105/joss.01143},
url = {https://doi.org/10.21105/joss.01143},
year = {2019},
publisher = {The Open Journal},
volume = {4},
number = {33},
pages = {1143},
author = {Ravin Kumar and Colin Carroll and Ari Hartikainen and Osvaldo Martin},
title = {ArviZ a unified library for exploratory analysis of Bayesian models in Python},
journal = {Journal of Open Source Software}
}
@article{PITecdf_fittest,
doi = {10.1007/s11222-022-10090-6},
url = {https://doi.org/10.1007%2Fs11222-022-10090-6},
year = {2022},
month = {mar},
publisher = {Springer Science and Business Media LLC},
volume = {32},
number = {2},
author = {Teemu Säilynoja and Paul-Christian Bürkner and Aki Vehtari},
title = {Graphical test for discrete uniformity and its applications in goodness-of-fit evaluation and multiple sample comparison},
journal = {Statistics and Computing}
}
@book{Lunn2012BugsBook,
title={The BUGS Book: A Practical Introduction to Bayesian Analysis},
author={Lunn, David and Jackson, Chris and Best, Nicky and Thomas, Andrew and Spiegelhalter, David},
isbn={9781584888499},
year={2012},
publisher={Chapman & Hall},
edition={1},
pages={400},
note={91 B/W Illustrations}
}
@article{UCLIcelandVolcano,
author = {Day, Simon and Edwards, Stephen and Fearnley, Carina and Kilburn, Christopher and Mcguire, Bill and Stanbrough, L and Wall, R and Delacroix, S and James, A and Smith, A and Sword-Daniels, Victoria and Tyler, N and Jones, Adrian and Roberts, F and Tan, PJ and Bailey, Eleanor and Gaunt, L and Sammonds, Peter and Vallianatos, Filippos and Guillas, S},
year = {2010},
month = {01},
pages = {},
title = {Volcanic Hazard from Iceland: analysis and implications of the Eyjafjallajokull eruption},
journal = {UCL INSTITUTE FOR RISK AND DISASTER REDUCTION}
}