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The BUGS Book
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Table of Contents

Introduction: Probability and Parameters
Probability
Probability distributions
Calculating properties of probability distributions
Monte Carlo integration

Monte Carlo Simulations Using BUGS
Introduction to BUGS
DoodleBUGS
Using BUGS to simulate from distributions
Transformations of random variables
Complex calculations using Monte Carlo
Multivariate Monte Carlo analysis
Predictions with unknown parameters

Introduction to Bayesian Inference
Bayesian learning
Posterior predictive distributions
Conjugate Bayesian inference
Inference about a discrete parameter
Combinations of conjugate analyses
Bayesian and classical methods

Introduction to Markov Chain Monte Carlo Methods
Bayesian computation
Initial values
Convergence
Efficiency and accuracy
Beyond MCMC

Prior Distributions
Different purposes of priors
Vague, `objective' and `reference' priors
Representation of informative priors
Mixture of prior distributions
Sensitivity analysis

Regression Models
Linear regression with normal errors
Linear regression with non-normal errors
Nonlinear regression with normal errors
Multivariate responses
Generalised linear regression models
Inference on functions of parameters
Further reading

Categorical Data
2 x 2 tables
Multinomial models
Ordinal regression
Further reading

Model Checking and Comparison
Introduction
Deviance
Residuals
Predictive checks and Bayesian p-values
Model assessment by embedding in larger models
Model comparison using deviances
Bayes factors
Model uncertainty
Discussion on model comparison
Prior-data conflict

Issues in Modelling
Missing data
Prediction
Measurement error
Cutting feedback
New distributions
Censored, truncated and grouped observations
Constrained parameters
Bootstrapping
Ranking

Hierarchical Models
Exchangeability
Priors
Hierarchical regression models
Hierarchical models for variances
Redundant parameterisations
More general formulations
Checking of hierarchical models
Comparison of hierarchical models
Further resources

Specialised Models
Time-to-event data
Time series models
Spatial models
Evidence synthesis
Differential equation and pharmacokinetic models
Finite mixture and latent class models
Piecewise parametric models
Bayesian nonparametric models

Different Implementations of BUGS
Introduction BUGS engines and interfaces
Expert systems and MCMC methods
Classic BUGS
WinBUGS
OpenBUGS
JAGS

A Appendix: BUGS Language Syntax
Introduction
Distributions
Deterministic functions
Repetition
Multivariate quantities
Indexing
Data transformations
Commenting

B Appendix: Functions in BUGS
Standard functions
Trigonometric functions
Matrix algebra
Distribution utilities and model checking
Functionals and differential equations
Miscellaneous

C Appendix: Distributions in BUGS
Continuous univariate, unrestricted range
Continuous univariate, restricted to be positive
Continuous univariate, restricted to a finite interval
Continuous multivariate distributions
Discrete univariate distributions
Discrete multivariate distributions

Bibliography

Index

About the Author

MRC Biostatistics Unit, Cambridge, UK Imperial College, London, UK Helsinki, Finland College School of Medicine, London, UK University of Bath, UK University of Minnesota, Minneapolis, Minnesota, USA Northwestern University, Evanston, Illinois, USA University of British Columbia, Vancouver, Canada

Reviews

"This is a beautiful book-it was a pleasure, and indeed great fun to read. ... The authors succeeded in writing a very nicely readable yet concise and carefully balanced text. ... It contains a lot of motivation, detailed explanations, necessary pieces of underlying theory, references to useful book-length treatments of various topics, and examples of the code illustrating how to implement concrete models in the BUGS language efficiently. ... this book also has a substantial pedagogical value. By reading this book carefully, redoing the examples, and thinking about them, one can learn a lot not only about BUGS, but also about Bayesian methods and statistics in general. ... highly recommended to a wide audience, from students of statistics [to] practicing statisticians to researchers from various fields."
-ISCB News, 57, June 2014

"... truly demonstrates the power and flexibility of the BUGS software and its broad range of applications, and that makes this book highly relevant not only for beginners but for advanced users as well. ... a notable addition to the growing range of introductory Bayesian textbooks that have been published within the last decade. It is unique in its focus on explicating state-of-the-art computational Bayesian strategies in the WinBUGS software. Thus, practitioners may use it as an excellent, didactically enhanced BUGS manual that, unlike ordinary software manuals, presents detailed explanations of the underlying models with references to relevant literature [and] worked examples, including excerpts of WinBUGS code, as well as graphical illustrations of results and critical discussions. No doubt, The BUGS Book will become a classic Bayesian textbook and provide invaluable guidance to practicing statisticians, academics, and students alike."
-Renate Meyer, Journal of Biopharmaceutical Statistics, 2014

"In this book the developers of BUGS reveal the power of the BUGS software and how it can be used in Bayesian statistical modeling and inference. Many people will find it very useful for self-learning or as a supplement for a Bayesian inference course."
-William M. Bolstad, Australian & New Zealand Journal of Statistics, 2013

"If a book has ever been so much desired in the world of statistics, it is for sure this one. ... the tens of thousands of users of WinBUGS are indebted to the leading team of the BUGS project for having eventually succeeded in finalizing the writing of this book and for making sure that the long-held expectations are not dashed. ... it reflects very well the aims and spirit of the BUGS project and is meant to be a manual `for anyone who would like to apply Bayesian methods to real-world problems.' ... strikes the right distance between advanced theory and pure practice. I especially like the numerous examples given in the successive chapters which always help readers to figure out what is going on and give them new ideas to improve their BUGS skills. ... The BUGS Book is not only a major textbook on a topical subject, but it is also a mandatory one for all statisticians willing to learn and analyze data with Bayesian statistics at any level. It will be the companion and reference book for all users (beginners or advanced) of the BUGS software. I have no doubt it will meet the same success as BUGS and become very soon a classic in the literature of computational Bayesian statistics."
-Jean-Louis Fouley, CHANCE, 2013

"... a two-in-one product that provides the reader with both a BUGS manual and a Bayesian analysis textbook, a combination that will likely appeal to many potential readers. ... The strength of The BUGS Book is its rich collection of ambitiously constructed and thematically arranged examples, which often come with snippets of code and printouts, as well as illustrative plots and diagrams. ... great value to many readers seeking to familiarize themselves with BUGS and its capabilities."
-Joakim Ekstroem, Journal of Statistical Software, January 2013

"MCMC freed Bayes from the shackles of conjugate priors and the curse of dimensionality; BUGS then brought MCMC-Bayes to the masses, yielding an astonishing explosion in the number, quality, and complexity of Bayesian inference over a vast array of application areas, from finance to medicine to data mining. The most anticipated applied Bayesian text of the last 20 years, The BUGS Book is like a wonderful album by an established rock supergroup: the pressure to deliver a high-quality product was enormous, but the authors have created a masterpiece well worth the wait. The book offers the perfect mix of basic probability calculus, Bayes and MCMC basics, an incredibly broad array of useful statistical models, and a BUGS tutorial and user manual complete with all the `tricks' one would expect from the team that invented the language. BUGS is the dominant Bayesian software package of the post-MCMC era, and this book ensures it will remain so for years to come by providing accessible yet comprehensive instruction in its proper use. A must-own for any working applied statistical modeler."
-Bradley P. Carlin, Professor and Head of Division of Biostatistics, University of Minnesota, Minneapolis, USA

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