Monte Carlo Methods in Bayesian Computation

1. Front Matter

   Pages i-xiii

   PDF

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

    PDF

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.

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

"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

• 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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