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Stability of Markov Chain Monte Carlo Methods by Kengo Kamatani
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Stability of Markov Chain Monte Carlo Methods

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Description

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.
Release date NZ
September 22nd, 2024
Audience
  • Professional & Vocational
Edition
1st ed. 2024
Illustrations
10 Illustrations, black and white; VI, 104 p. 10 illus.
Pages
104
ISBN-13
9784431552567
Product ID
22762265

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