This book examines advanced Bayesian computational methods. It presents methods for sampling from posterior distributions and discusses how to compute posterior quantities of interest using Markov chain Monte Carlo (MCMC) samples. This book examines each of these issues in detail and heavily focuses on computing various posterior summaries from a given MCMC sample. Several topics are addressed, including techniques for MCMC sampling, Monte Carlo methods for estimation of posterior expectations, improving simulation accuracy, marginal posterior density estimation, estimation of normalizing constants, constrained parameter problems, highest posterior density interval calculations, computation of posterior modes, and posterior computations for proportional hazards models and Dirichlet process models. The authors also discuss computations involving model comparisons, including both nested and nonnested models, marginal likelihood methods, ratios of normalizing constants, Bayes factors, the Savage-Dickey density ratio, stochastic search variable selection, Bayesian model averaging, the reverse jump algorithm, and model adequacy using predictive and latent residual approaches.

The book presents an equal mixture of theory and applications involving real data. It is intended as a graduate textbook or a reference book for a one semester course at the advanced masters or Ph.D. level. It would also serve as a useful reference book for applied or theoretical researchers as well as practitioners.

Ming-Hui Chen is Associate Professor of Mathematical Sciences at Worcester Polytechnic Institute; Qi-Man Shao is Assistant Professor of Mathematics at the University of Oregon; and Joseph G. Ibrahim is Associate Professor of Biostatistics at the Harvard School of Public Health and Dana-Farber Cancer Institute.