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Monte Carlo Methods in Bayesian Computation

  • Book
  • © 2000

Overview

Authors:
  1. Ming-Hui Chen

    1. Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, USA

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  2. Qi-Man Shao

    1. Department of Mathematics, University of Oregon, Eugene, USA

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    You can also search for this author in PubMed   Google Scholar

  3. Joseph G. Ibrahim

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

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    You can also search for this author in PubMed   Google Scholar

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

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Introduction

    • Ming-Hui Chen, Qi-Man Shao, Joseph G. Ibrahim
    Pages 1-18

  3. Markov Chain Monte Carlo Sampling

    • Ming-Hui Chen, Qi-Man Shao, Joseph G. Ibrahim
    Pages 19-66

  4. Basic Monte Carlo Methods for Estimating Posterior Quantities

    • Ming-Hui Chen, Qi-Man Shao, Joseph G. Ibrahim
    Pages 67-93

  5. Estimating Marginal Posterior Densities

    • Ming-Hui Chen, Qi-Man Shao, Joseph G. Ibrahim
    Pages 94-123

  6. Estimating Ratios of Normalizing Constants

    • Ming-Hui Chen, Qi-Man Shao, Joseph G. Ibrahim
    Pages 124-190

  7. Monte Carlo Methods for Constrained Parameter Problems

    • Ming-Hui Chen, Qi-Man Shao, Joseph G. Ibrahim
    Pages 191-212

  8. Computing Bayesian Credible and HPD Intervals

    • Ming-Hui Chen, Qi-Man Shao, Joseph G. Ibrahim
    Pages 213-235

  9. Bayesian Approaches for Comparing Nonnested Models

    • Ming-Hui Chen, Qi-Man Shao, Joseph G. Ibrahim
    Pages 236-266

  10. Bayesian Variable Selection

    • Ming-Hui Chen, Qi-Man Shao, Joseph G. Ibrahim
    Pages 267-306

  11. Other Topics

    • Ming-Hui Chen, Qi-Man Shao, Joseph G. Ibrahim
    Pages 307-355

  12. Back Matter

    Pages 356-387
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Keywords

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.

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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