Markov Chain Monte Carlo in PracticeW.R. Gilks, S. Richardson, David Spiegelhalter In a family study of breast cancer, epidemiologists in Southern California increase the power for detecting a gene-environment interaction. In Gambia, a study helps a vaccination program reduce the incidence of Hepatitis B carriage. Archaeologists in Austria place a Bronze Age site in its true temporal location on the calendar scale. And in France, researchers map a rare disease with relatively little variation. Each of these studies applied Markov chain Monte Carlo methods to produce more accurate and inclusive results. General state-space Markov chain theory has seen several developments that have made it both more accessible and more powerful to the general statistician. Markov Chain Monte Carlo in Practice introduces MCMC methods and their applications, providing some theoretical background as well. The authors are researchers who have made key contributions in the recent development of MCMC methodology and its application. Considering the broad audience, the editors emphasize practice rather than theory, keeping the technical content to a minimum. The examples range from the simplest application, Gibbs sampling, to more complex applications. The first chapter contains enough information to allow the reader to start applying MCMC in a basic way. The following chapters cover main issues, important concepts and results, techniques for implementing MCMC, improving its performance, assessing model adequacy, choosing between models, and applications and their domains. Markov Chain Monte Carlo in Practice is a thorough, clear introduction to the methodology and applications of this simple idea with enormous potential. It shows the importance of MCMC in real applications, such as archaeology, astronomy, biostatistics, genetics, epidemiology, and image analysis, and provides an excellent base for MCMC to be applied to other fields as well. |
Contents
for some function of interest f Here we allow for the possibility that | 4 |
a case study in MCMC methods | 21 |
BUGS | 42 |
Introduction to general statespace Markov chain theory | 59 |
Full conditional distributions | 75 |
Strategies for improving MCMC | 89 |
Implementing MCMC | 115 |
Inference and monitoring convergence | 131 |
Bayesian model comparison via jump diffusions | 215 |
Estimation and optimization of functions | 241 |
method and application | 259 |
Generalized linear mixed models | 275 |
Hierarchical longitudinal modelling | 303 |
Medical monitoring | 321 |
Bayesian mapping of disease | 359 |
Measurement error | 401 |
Andrew Gelman Department of Statistics | 142 |
Model determination using samplingbased methods | 145 |
Hypothesis testing and model selection | 163 |
Model checking and model improvement | 189 |
Stochastic search variable selection | 203 |
George MSIS Department | 214 |
Other editions - View all
Markov Chain Monte Carlo in Practice W.R. Gilks,S. Richardson,David Spiegelhalter Limited preview - 1995 |
Markov Chain Monte Carlo in Practice W. R. Gilks,S. Richardson,D. J. Spiegelhalter No preview available - 2013 |
Common terms and phrases
A. F. M. Smith A. P. Dawid analysis approximation Bayes factor Bayesian inference Bayesian Statistics Besag calculated Carlo in Practice Chain Monte Carlo Chapman & Hall components computational convergence covariates D. J. Spiegelhalter Dawid and A. F. M. denotes discussion eds J. M. Bernardo eds W. R. Gilks ergodic estimate evaluation example Figure full conditional distributions function Gaussian Gelfand Geyer Gibbs sampler gibbsit hyperparameters independent irreducible J. R. Statist London marginal likelihood Markov Chain Monte matrix maximum likelihood MCMC MCMC methods Metropolis algorithm Metropolis-Hastings algorithm mixing mixture Monte Carlo methods multivariate number of iterations observed output parameterization parameters posterior distribution Practice eds W. R. prior distribution probability problem Raftery random effects random-effects model recurrent regression rejection sampling reparameterization Richardson and D. J. Roberts Section sequence starting values state-space stationary distribution stochastic target distribution theorem Tierney tion titre updating variable variance vector volume