Stability of Markov Chain Monte Carlo Methods
Seiten
2024
|
1st ed. 2024
Springer Verlag, Japan
978-4-431-55256-7 (ISBN)
Springer Verlag, Japan
978-4-431-55256-7 (ISBN)
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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 | 13.12.2024 |
---|---|
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 |
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 |
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