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Monte Carlo Methods in Bayesian Computation

  • Book
  • © 2000

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Part of the book series: Springer Series in Statistics (SSS)

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About this book

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.

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Table of contents (10 chapters)

Reviews

"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

Authors and Affiliations

  • Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, USA

    Ming-Hui Chen

  • Department of Mathematics, University of Oregon, Eugene, USA

    Qi-Man Shao

  • Department of Biostatistics, Harvard School of Public Health and Dana-Farber Cancer Institute, Boston, USA

    Joseph G. Ibrahim

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