Stability of Markov Chain Monte Carlo Methods, 1st ed. 2024
JSS Research Series in Statistics Series

This book presents modern techniques for the analysis of Markov chain Monte Carlo (MCMC) methods. A central focus is the study of the number of iteration of MCMC and the relation to some indices, such as the number of observation, or the number of dimension of the parameter space. The approach in this book is based on the theory of convergence of probability measures for two kinds of randomness: observation randomness and simulation randomness. This method provides in particular the optimal bounds for the random walk Metropolis algorithm and useful asymptotic information on the data augmentation algorithm. Applications are given to the Bayesian mixture model, the cumulative probit model, and to some other categorical models. This approach yields new subjects, such as the degeneracy problem and optimal rate problem of MCMC. Containing asymptotic results of MCMC under a Bayesian statistical point of view, this volume will be useful to practical and theoretical researchers and to graduatestudents in the field of statistical computing.

1  Introductio. -2  Consistency of the Markov chain Monte Carlo method.- 3  Invariant Measures and Related Topics.- 4  Applications.

Suits MCMC users with a statistical background is the first book completely devoted to the study of MCMC from a statistical point of view Provides a unified view of the theory of many MCMC methods