Synopses & Reviews
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 quantities of interest from a given MCMC sample. Several topics are addressed, including techniques for MCMC sampling, Monte Carlo methods for estimation of posterior quantities, 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 computions involving model comparisons, including both nested and non-nested 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. The book 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, Qu-Man Shao is Assistant Professor of Mathematics at the University of Oregon. Joseph G. Ibrahim is Associate Professor of Biostatistics at the Harvard School of Public Health and Dana-Farber Cancer Institute.
Review
"This book combines the theory topics with good computer and application examples from the field of food science, agriculture, cancer and others. The volume will provide an excellent research resource for statisticians with an interest in computer intensive methods for modelling with different sorts of prior information." A.V. Tsukanov in "Short Book Reviews", Vol. 20/3, December 2000
Synopsis
With an equal mix of theory and applications involving real data, this book presents the theoretical background of the Markov chain Monte Carlo (MCMC) methods and examines advanced Bayesian computational methods. 20 illus.
Synopsis
Sampling from the posterior distribution and computing posterior quanti- ties of interest using Markov chain Monte Carlo (MCMC) samples are two major challenges involved in advanced Bayesian computation. This book examines each of these issues in detail and focuses heavily on comput- ing various posterior quantities of interest from a given MCMC sample. Several topics are addressed, including techniques for MCMC sampling, Monte Carlo (MC) methods for estimation of posterior summaries, improv- ing simulation accuracy, marginal posterior density estimation, estimation of normalizing constants, constrained parameter problems, Highest Poste- rior Density (HPD) interval calculations, computation of posterior modes, and posterior computations for proportional hazards models and Dirichlet process models. Also extensive discussion is given for computations in- volving model comparisons, including both nested and nonnested models. Marginal likelihood methods, ratios of normalizing constants, Bayes fac- tors, the Savage-Dickey density ratio, Stochastic Search Variable Selection (SSVS), Bayesian Model Averaging (BMA), the reverse jump algorithm, and model adequacy using predictive and latent residual approaches are also discussed. The book presents an equal mixture of theory and real applications.
Synopsis
Bayesian statistics is one of the active research areas in statistics. This book provides the theoretical background behind the most important recent development, Markov chain Monte Carlos methods.
Synopsis
Dealing with methods for sampling from posterior distributions and how to compute posterior quantities of interest using Markov chain Monte Carlo (MCMC) samples, this book addresses such topics as 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 model comparisons, including both nested and non-nested 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, and is intended as a graduate textbook or a reference book for a one-semester course at the advanced masters or Ph.D. level. It will also serve as a useful reference for applied or theoretical researchers as well as practitioners.
Table of Contents
Introduction * Markov Chain Monte Carlo Sampling * Basic Monte Carlo Methods for Estimating Posterior Quantities * Estimating Marginal Posterior Densities * Estimating Ratios of Normalizing Constants * Monte Carlo Methods for Constrained Parameter Problems * Computing Bayesian Credible and HPD Intervals * Bayesian Approaches for Comparing Non-Nested Models * Bayesian Variable Section * Other Topics