Markov Chain Monte Carlo in Practice
W.R. Gilks, S. Richardson, David Spiegelhalter
CRC Press, Dec 1, 1995 - Mathematics - 512 pages
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.
a case study in MCMC methods
Markov chain concepts related to sampling algorithms
Introduction to general statespace Markov chain theory
Full conditional distributions
Strategies for improving MCMC
Inference and monitoring convergence
Andrew Gelman Department of Statistics
George MSIS Department
Bayesian model comparison via jump diffusions
Estimation and optimization of functions
method and application
Generalized linear mixed models
Bayesian mapping of disease
Model determination using samplingbased methods
Hypothesis testing and model selection
Model checking and model improvement
Stochastic search variable selection
Gibbs sampling methods in genetics
inference and estimation
A. F. M. Smith A. P. Dawid analysis applications approach approximation assume Bayes factor Bayesian inference Bayesian Statistics Besag calculated Carlo in Practice Chain Monte Carlo Chapman fc Hall components computation convergence covariates D. J. Spiegelhalter dataset denotes depend described discussion disease eds J. M. Bernardo eds W. R. Gilks ergodic error estimate evaluation example Figure full conditional distributions function Gaussian Gelfand Gelman genotypes Geyer Gibbs sampler gibbsit hierarchical hyperparameters independent irreducible J. R. Statist jump London marginal likelihood Markov Chain Monte matrix maximum likelihood MCMC MCMC methods mean Metropolis-Hastings algorithm missing data mixing mixture model multivariate normal distribution observed parameterization parameters posterior distribution posterior probability Practice eds W. R. predictive density prior distribution problem proposal Raftery random effects random-effects model regression rejection sampling reparameterization Richardson and D. J. Roberts Rubin Section sequence simulation stationary distribution stochastic target distribution tion updating variable variance vector volume