Markov Chain Monte Carlo : Stochastic Simulation for Bayesian Inference, Second Edition book cover
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Markov Chain Monte Carlo
Stochastic Simulation for Bayesian Inference, Second Edition




ISBN 9781584885870
Published May 10, 2006 by Chapman and Hall/CRC
342 Pages 44 B/W Illustrations

 
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Book Description

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

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.

Table of Contents

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

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Reviews

"The new edition of the book, with its updated and additional materials, is still a great choice as at textbook for Bayesian computation and inference courses in a graduate program in computational and applied statistics. It will also be considered as one of the best textbooks for a Bayesian computational course to nonstatisticians, including social scientists and engineers."

– Debajyoti Sinha, Florida State University, in JASA, March 2009

“The second edition of this book is well written and builds on the
first edition … The addition of an associated website is a valuable resource that contains many R scripts, allowing readers to quickly and easily test different approaches on their desired models with minimal effort. Coupling this with the depth of examples and references provided, this text provides an excellent first graduate text on MCMC methods. … The book is certainly another fine addition on the literature on MCMC and should be used by anyone interested in gaining a solid foundation in MCMC methods and algorithms. …”
—Gareth Peters (University of New South Wales), Statistics in Medicine, 2008

“… one of the most comprehensive and readable texts on stochastic simulation using the technique of Markov chain Monte Carlo. … this second edition has been extensively updated to include the recent literature. New sections on spatial modeling and model adequacy have now been included, together with more illustrative material. Many of the computer codes written in R and WinBUGS … are available for download from the web. This enhances the utility of the book, both as a reference for researchers and a text on modern Bayesian computation and Bayesian inference courses for students.”
—C.M. O’Brien (CEFAS Lowestoft Laboratory, UK), ISI Short Book Reviews

“…The book may be quite useful as a first book on MCMC. … The treatment is nontechnical, easily read, and may be a good starting point for a statistician with little or no prior knowledge of MCMC. There is also nonstandard material. I found the material on dynamical models (including non-Gaussian ones) particularly interesting. …”
—Søren Feodor Nielsen (University of Copenhagen), Journal of Applied Statistics, Vol. 34, No. 7, December 2007

“…The book does have an impressive set of exercises … it would be appropriate for a course that wants to focus on using MCMC to solve applied Bayesian inference problems.”
—Galin L. Jones, Mathematical Reviews, 2007j

Praise for the First Edition:
 “…a must for every research library, and should be given serious consideration for use as a graduate text.”
ISI Short Book Reviews

“…nicely focused, elementary-level coverage…makes this book a suitable choice for an introductory course.”
Journal of the ASA, March 2000