Monte Carlo Methods in Bayesian Computation

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

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

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Ming-Hui Chen, Qi-Man Shao, Joseph G. Ibrahim
    Pages 1-18
  3. Ming-Hui Chen, Qi-Man Shao, Joseph G. Ibrahim
    Pages 19-66
  4. Ming-Hui Chen, Qi-Man Shao, Joseph G. Ibrahim
    Pages 67-93
  5. Ming-Hui Chen, Qi-Man Shao, Joseph G. Ibrahim
    Pages 94-123
  6. Ming-Hui Chen, Qi-Man Shao, Joseph G. Ibrahim
    Pages 124-190
  7. Ming-Hui Chen, Qi-Man Shao, Joseph G. Ibrahim
    Pages 191-212
  8. Ming-Hui Chen, Qi-Man Shao, Joseph G. Ibrahim
    Pages 213-235
  9. Ming-Hui Chen, Qi-Man Shao, Joseph G. Ibrahim
    Pages 236-266
  10. Ming-Hui Chen, Qi-Man Shao, Joseph G. Ibrahim
    Pages 267-306
  11. Ming-Hui Chen, Qi-Man Shao, Joseph G. Ibrahim
    Pages 307-355
  12. Back Matter
    Pages 356-387

About this book

Introduction

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.

Keywords

Bayesian Computation Estimator Likelihood Logistic Regression Markov Chain Monte Carlo Methods Time series statistics

Authors and affiliations

  • Ming-Hui Chen
    • 1
  • Qi-Man Shao
    • 2
  • Joseph G. Ibrahim
    • 3
  1. 1.Department of Mathematical SciencesWorcester Polytechnic InstituteWorcesterUSA
  2. 2.Department of MathematicsUniversity of OregonEugeneUSA
  3. 3.Department of BiostatisticsHarvard School of Public Health and Dana-Farber Cancer InstituteBostonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-1276-8
  • Copyright Information Springer-Verlag New York, Inc. 2000
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-7074-4
  • Online ISBN 978-1-4612-1276-8
  • Series Print ISSN 0172-7397
  • About this book