Markov chain Monte Carlo (MCMC) methods can be used for inference in complex statistical models. Although MCMC techniques have been used in statistical physics for many years, their usefulness for general statistical modelling has only recently been appreciated. The literature on MCMC methodology and its applications is scattered and rapidly expanding; this book draws together contributions from authorities in the field, and fills the urgent need to communicate the state of the art to a general statistical audience. Emphasis is placed on practice rather than theory although fundamental theoretical concepts are discussed. The issues covered arise in real applications such as archaeology, astronomy, biostatistics, genetics, epidemiology and image analysis. This introductory level text is suitable for applied statisticians, biostatisticians and statistically orientated epidemiologists and computer scientists.
• practically oriented with real applications
• draws together contributions from leading authorities in a field which is currently a `hot' topic

Table of Contents
Introducing Markov chain Monte Carlo - W. R. Gilks, S. Richardson and D. J. Spiegelhalter. Introduction. The problem. Markov chain Monte Carlo. Implementation. Discussion. Hepatitis B: a case study in MCMC methods - D. J. Spiegelhalter, N. G. Best, W. R. Gilks and H. Inskip. Introduction. Hepatitis B immunization. Modelling. Fitting a model using Gibbs sampling. Model elaboration. Conclusion. Appendix: BUGS. Markov chain concepts related to sampling algorithms - G. O. Roberts. Introduction. Markov chains. Rates of convergence. Estimation. The Gibbs sampler and Metropolis-Hastings algorithm. Introduction to general state-space Markov chain theory - L. Tierney. Introduction . Notation and definitions. Irreducibility, recurrence and convergence. Harris recurrence. Mixing rates and central limit theorems. Regeneration. Discussion. Full conditional distributions - W. R. Gilks. Introduction. Deriving full conditional distributions. Sampling from full conditional distributions. Discussion. Strategies for improving MCMC - W. R. Gilks and G. O. 0oberts. Introduction. Reparameterization. Random and adaptive direction sampling. Modifying the stationary distribution. Methods based on continuous-time processes. Discussion. Implementing MCMC A. E. Raftery and S. M. Lewis. Introduction. Determining the number of iterations. Software and implementation. Output analysis. Generic Metropolis algorithms. Discussion. Inference and monitoring convergence A. Gelman. Difficulties in inference from Markov chain simulation. The risk of undiagnosed slow convergence. Multiple sequences and overdispersed starting points. Monitoring convergence using simulation output. Output analysis for inference. Output analysis for improving efficiency. Model determination using sampling-based methods - A. E. Gelfand. Introduction. Classical approaches. The Bayesian perspective and the Bayes factor. Alternative predictive distributions. How to use predictive distributions. Computational issues. An example. Discussion. Hypothesis testing and model selection - A. E. Raftery. Introduction. Uses of Bayes factors. Marginal likelihood estimation by importance sampling. Marginal likelihood estimation using maximum likelihood. Application: how many components in a mixture? Discussion. Appendix: S-PLUS code for the Laplace-Metropolis estimator. Model checking and model improvement - A. Gelman and X.-L. Meng. Introduction. Model checking using posterior predictive simulation. Model improvement via expansion. Example: hierarchical mixture modelling of reaction times. Stochastic search variable selection E. I. George and r. E. McCulloch. Introdution. A hierarchical Bayesian model for variable selection. Searching the posterior by Gibbs sampling. Extensions. Constructing stock portfolios with SSVS. Discussion. Bayesian model comparison via jump diffusions - D. B. Philips and A. F. M. Smith. Introduction. Model choice. Jump-diffusion sampling. Mixture deconvolution. Object recognition. Variable selection. Change-point identification. Conclusions. Estimation and optimization of functions - C. J. Geyer. Non-Bayesian applications of MCMC. Monte Carlo optimization. Monte Carlo likelihood analysis. Normalizing-constant families. Missing data. Decision theory. Which sampling distribution? Importance sampling. Discussion. Stochastic EM: method and application - J. Diebolt and E. H. S. Ip. Introduction. The EM algorithm. The stochastic EM algorithm. Examples. Generalized linear mixed models - D. G. Clayton. Introduction. Generalized linear models (GLM). Bayesian estimation of GLMs. Gibbs sampling for GLMs. Generalized linear mixed models (GLMMs). Specification of random-effect distributions. Hyperpriors and the estimation of hyperparameters. Some examples. Discussion. Hierarchical longitudinal modelling - B. P. Carlin. Introudction. Clinical background. Model detail and MCMC implementation. Results. Summary and discussion. Medical monitoring - C. Berzuini. Introduction. Modelling medical monitoring. Computing posterior distributions. Forecasting. Model criticism. Illustrative application. Discussion. MCMC for nonlinear hierarchical models - J. E. Bennett, A. Racine-Poon and J. C. Wakefield. Introduction. Imlementing MCMC. Comparison of strategies. A case study from pharmacokinetics-pharmacodynamics. Extensions and discussion. Bayesian mapping of disease - A. Mollie. Introduction. Hypotheses and notation. Maximum likelihood estimation of relative risks. Hierarchical Bayesian model of relative risks. Empirical bayes estimation of relative risks. Fully Bayesian estimation of relative risks. Discussion. MCMC in image analysis - P. J. Green. Introduction. The relevance of MCMC to image analysis. Image models at differenct levels. Methodological innovations in MCMC stimulated by imaging. Discussion. Measurement error - S. Richardson. Introduction. Conditional-independence modelling. Illustrative examples. Discussion. Introduction. Standard methods in genetics. Gibbs sampling approaches. MCMC maximum likelihood. Application to a family study of breast cancer. Conclusions. Mixtures of distributions: inference and estimation - C. P. Robert. Introduction. The missing data structure. Gibbs sampling implementation. Convergence of the algorithm. Testing for mixtures. Infinite mixtures and other extensions. An archaeological example: radiocarbon dating - C. Litton and C. Buck. Introduction. Background to radiocarbon dating. Archaeological problems and questions . Illustrative examples. Discussion. Index.

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