Bayesian statistics is one of the active research areas in statistics. This book provides the theoretical background behind the most important recent development, Markov chain Monte Carlos methods.

Includes supplementary material: sn.pub/extras

Inhalt
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 Controlling Simulation Errors.- Exercises.- 4 Estimating Marginal Posterior Densities.- 4.1 Marginal Posterior Densities.- 4.2 Kernel Methods.- 4.3 IWMDE Methods.- 4.4 Illustrative Examples.- 4.5 Performance Study Using the Kullback-Leibler Divergence.- Exercises.- 5 Estimating Ratios of Normalizing Constants.- 5.1 Introduction.- 5.2 Importance Sampling.- 5.3 Bridge Sampling.- 5.4 Path Sampling.- 5.5 Ratio Importance Sampling.- 5.6 A Theoretical Illustration.- 5.7 Computing Simulation Standard Errors.- 5.8 Extensions to Densities with Different Dimensions.- 5.9 Estimation of Normalizing Constants After Transformation.- 5.10 Other Methods.- 5.11 An Application of Weighted Monte Carlo Estimators.- 5.12 Discussion.- Exercises.- 6 Monte Carlo Methods for Constrained Parameter Problems.- 6.1 Constrained Parameter Problems.- 6.2 Posterior Moments and Marginal Posterior Densities.- 6.3 Computing Normalizing Constants for Bayesian Estimation.- 6.4 Applications.- 6.5 Discussion.- Exercises.- 7 Computing Bayesian Credible and HPD Intervals.- 7.1 Bayesian Credible and HPD Intervals.- 7.2 EstimatingBayesian Credible Intervals.- 7.3 Estimating Bayesian HPD Intervals.- 7.4 Extension to the Constrained Parameter Problems.- 7.5 Numerical Illustration.- 7.6 Discussion.- Exercises.- 8 Bayesian Approaches for Comparing Nonnested Models.- 8.1 Marginal Likelihood Approaches.- 8.2 Scale Mixtures of Multivariate Normal Link Models.- 8.3 Super-Model or Sub-Model Approaches.- 8.4 Criterion-Based Methods.- 9 Bayesian Variable Selection.- 9.1 Variable Selection for Logistic Regression Models.- 9.2 Variable Selection for Time Series Count Data Models.- 9.3 Stochastic Search Variable Selection.- 9.4 Bayesian Model Averaging.- 9.5 Reversible Jump MCMC Algorithm for Variable Selection.- Exercises.- 10 Other Topics.- 10.1 Bayesian Model Adequacy.- 10.2 Computing Posterior Modes.- 10.3 Bayesian Computation for Proportional Hazards Models.- 10.4 Posterior Sampling for Mixture of Dirichlet Process Models.- Exercises.- References.- Author Index.