Monte Carlo Methods in Bayesian Computation

ISBN-13: 9781461270744 / Angielski / Miękka / 2012 / 387 str.

Ming-Hui Chen; Qi-Man Shao; Joseph G. Ibrahim

Opis

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.

Recenzje

"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

Spis treści

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

O autorze

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.