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Stability of Markov Chain Monte Carlo Methods

  • Book
  • Sep 2024

Overview

Authors:
  1. Kengo Kamatani

    1. Osaka University Graduate School of Engineering Science, Toyonaka, Japan

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  • 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

Part of the book series: SpringerBriefs in Statistics (BRIEFSSTATIST)

Part of the book sub series: JSS Research Series in Statistics (JSSRES)

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Keywords

  • Bayesian Statistics
  • Ergodicity
  • Large sample theory
  • Markov chain Monte Carlo
  • Stochastic Process

About this book

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.

Authors and Affiliations

  • Osaka University Graduate School of Engineering Science, Toyonaka, Japan

    Kengo Kamatani

Bibliographic Information

  • Book Title: Stability of Markov Chain Monte Carlo Methods

  • Authors: Kengo Kamatani

  • Series Title: SpringerBriefs in Statistics

  • Publisher: Springer Tokyo

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Author(s), under exclusive licence to Springer Japan KK 2024

  • Softcover ISBN: 978-4-431-55256-7Due: 22 September 2024

  • eBook ISBN: 978-4-431-55257-4Due: 22 September 2024

  • Series ISSN: 2191-544X

  • Series E-ISSN: 2191-5458

  • Edition Number: 1

  • Number of Pages: VI, 104

  • Number of Illustrations: 10 b/w illustrations

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