Stability of Markov Chain Monte Carlo Methods

Kengo Kamatani (Autor)

Buch | Softcover

104 Seiten

2025 | 1st ed. 2024
Springer Verlag, Japan
978-4-431-55256-7 (ISBN)

Noch nicht erschienen - erscheint am 24.03.2025
Versandkostenfrei
Auch auf Rechnung

Artikel merken

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.

Erscheint lt. Verlag	24.3.2025
Reihe/Serie	JSS Research Series in Statistics
	JSS Research Series in Statistics
	SpringerBriefs in Statistics
	SpringerBriefs in Statistics
Zusatzinfo	10 Illustrations, black and white; VI, 104 p. 10 illus.
Verlagsort	Tokyo
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Computerprogramme / Computeralgebra
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	Bayesian Statistics • Ergodicity • Large Sample Theory • Markov Chain Monte Carlo • Stochastic process
ISBN-10	4-431-55256-1 / 4431552561
ISBN-13	978-4-431-55256-7 / 9784431552567
Zustand	Neuware