Monte Carlo Methods in Bayesian Computation [Hardcover]

Sampling from the posterior distribution and computing posterior quanti? ties of interest using Markov chain Monte Carlo (MCMC) samples are two major challenges involved in advanced Bayesian computation. This book examines each of these issues in detail and focuses heavily on comput? ing various posterior quantities of interest from a given MCMC sample. Several topics are addressed, including techniques for MCMC sampling, Monte Carlo (MC) methods for estimation of posterior summaries, improv? ing simulation accuracy, marginal posterior density estimation, estimation of normalizing constants, constrained parameter problems, Highest Poste? rior Density (HPD) interval calculations, computation of posterior modes, and posterior computations for proportional hazards models and Dirichlet process models. Also extensive discussion is given for computations in? volving model comparisons, including both nested and nonnested models. Marginal likelihood methods, ratios of normalizing constants, Bayes fac? tors, the Savage-Dickey density ratio, Stochastic Search Variable Selection (SSVS), Bayesian Model Averaging (BMA), the reverse jump algorithm, and model adequacy using predictive and latent residual approaches are also discussed. The book presents an equal mixture of theory and real applications.1 Introduction.- 1.1 Aims.- 1.2 Outline.- 1.3 Motivating Examples.- 1.4 The Bayesian Paradigm.- Exercises.- 2 Markov Chain Monte Carlo Sampling.- 2.1 Gibbs Sampler.- 2.2 Metropolis-Hastings Algorithm.- 2.3 Hit-and-Run Algorithm.- 2.4 Multiple-Try Metropolis Algorithm.- 2.5 Grouping, Collapsing, and Reparameterizations.- 2.6 Acceleration Algorithms for MCMC Sampling.- 2.7 Dynamic Weighting Algorithm.- 2.8 Toward Black-Box Sampling.- 2.9 Convergence Diagnostics.- Exercises.- 3 Basic Monte Carlo Methods for Estimating Posterior Quantities.- 3.1 Posterior Quantities.- 3.2 Basic Monte Carlo Methods.- 3.3 Simulation Standard Error Estimation.- 3.4 Improving Monte Carlo Estimates.- 3.5 Conlƒv