A First Course in Bayesian Statistical Methods

Peter D. Hoff (auth.)0387922997, 9780387922997, 9780387924076, 0387924078

This book provides a compact self-contained introduction to the theory and application of Bayesian statistical methods. The book is accessible to readers having a basic familiarity with probability, yet allows more advanced readers to quickly grasp the principles underlying Bayesian theory and methods. The examples and computer code allow the reader to understand and implement basic Bayesian data analyses using standard statistical models and to extend the standard models to specialized data analysis situations. The book begins with fundamental notions such as probability, exchangeability and Bayes’ rule, and ends with modern topics such as variable selection in regression, generalized linear mixed effects models, and semiparametric copula estimation. Numerous examples from the social, biological and physical sciences show how to implement these methodologies in practice.

Monte Carlo summaries of posterior distributions play an important role in Bayesian data analysis. The open-source R statistical computing environment provides sufficient functionality to make Monte Carlo estimation very easy for a large number of statistical models and example R-code is provided throughout the text. Much of the example code can be run “as is” in R, and essentially all of it can be run after downloading the relevant datasets from the companion website for this book.

Peter Hoff is an Associate Professor of Statistics and Biostatistics at the University of Washington. He has developed a variety of Bayesian methods for multivariate data, including covariance and copula estimation, cluster analysis, mixture modeling and social network analysis. He is on the editorial board of the Annals of Applied Statistics.

Table of contents :
Front Matter….Pages i-viii
Introduction and examples….Pages 1-12
Belief, probability and exchangeability….Pages 13-30
One-parameter models….Pages 31-52
Monte Carlo approximation….Pages 53-65
The normal model….Pages 67-87
Posterior approximation with the Gibbs sampler….Pages 89-104
The multivariate normal model….Pages 105-123
Group comparisons and hierarchical modeling….Pages 125-147
Linear regression….Pages 149-170
Nonconjugate priors and Metropolis-Hastings algorithms….Pages 171-193
Linear and generalized linear mixed effects models….Pages 195-207
Latent variable methods for ordinal data….Pages 209-223
Back Matter….Pages 225-270