While there have been few theoretical contributions on the Markov Chain Monte Carlo (MCMC) methods in the past decade, current understanding and application of MCMC to the solution of inference problems has increased by leaps and bounds. Incorporating changes in theory and highlighting new applications, "Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, Second Edition" presents a concise, accessible, and comprehensive introduction to the methods of this valuable simulation technique. The second edition includes access to an internet site that provides the code, written in R and WinBUGS, used in many of the previously existing and new examples and exercises. More importantly, the self-explanatory nature of the codes will enable modification of the inputs to the codes and variation on many directions will be available for further exploration. Major changes from the previous edition: more examples with discussion of computational details in chapters on Gibbs sampling and Metropolis-Hastings algorithms Recent developments in MCMC, including reversible jump, slice sampling, bridge sampling, path sampling, multiple-try, and delayed rejection; discussion of computation using both R and WinBUGS; additional exercises and selected solutions within the text, with all data sets and software available for download from the Web Sections on spatial models and model adequacy; and the self-contained text units make MCMC accessible to scientists in other disciplines as well as statisticians. The book will appeal to everyone working with MCMC techniques, especially research and graduate statisticians and biostatisticians, and scientists handling data and formulating models. The book has been substantially reinforced as a first reading of material on MCMC and, consequently, as a textbook for modern Bayesian computation and Bayesian inference courses.
INTRODUCTION
STOCHASTIC SIMULATION
Introduction
Generation of Discrete Random Quantities
Generation of Continuous Random Quantities
Generation of Random Vectors and Matrices
Resampling Methods
Exercises
BAYESIAN INFERENCE
Introduction
Bayes' Theorem
Conjugate Distributions
Hierarchical Models
Dynamic Models
Spatial Models
Model Comparison
Exercises
APPROXIMATE METHODS OF INFERENCE
Introduction
Asymptotic Approximations
Approximations by Gaussian Quadrature
Monte Carlo Integration
Methods Based on Stochastic Simulation
Exercises
MARKOV CHAINS
Introduction
Definition and Transition Probabilities
Decomposition of the State Space
Stationary Distributions
Limiting Theorems
Reversible Chains
Continuous State Spaces
Simulation of a Markov Chain
Data Augmentation or Substitution Sampling
Exercises
GIBBS SAMPLING
Introduction
Definition and Properties
Implementation and Optimization
Convergence Diagnostics
Applications
MCMC-Based Software for Bayesian Modeling
Appendix 5.A: BUGS Code for Example 5.7
Appendix 5.B: BUGS Code for Example 5.8
Exercises
METROPOLIS-HASTINGS ALGORITHMS
Introduction
Definition and Properties
Special Cases
Hybrid Algorithms
Applications
Exercises
FURTHER TOPICS IN MCMC
Introduction
Model Adequacy
Model Choice: MCMC Over Model and Parameter Spaces
Convergence Acceleration
Exercises
References
Author Index
Subject Index
