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Ergodicity of Markov chain Monte Carlo with reversible proposal

Part of: Probabilistic methods, simulation and stochastic differential equations Markov processes

Published online by Cambridge University Press:  22 June 2017

K. Kamatani
K. Kamatani*
Affiliation:
Osaka University
*
* Postal address: Graduate School of Engineering Science and Center for Mathematical Modeling and Data Science, Osaka University, 1-3 Machikaneyama-cho, Toyonaka, Osaka 560-8531, Japan. Email address: kamatani@sigmath.es.osaka-u.ac.jp
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Abstract

We describe the ergodic properties of some Metropolis–Hastings algorithms for heavy-tailed target distributions. The results of these algorithms are usually analyzed under a subgeometric ergodic framework, but we prove that the mixed preconditioned Crank–Nicolson (MpCN) algorithm has geometric ergodicity even for heavy-tailed target distributions. This useful property comes from the fact that, under a suitable transformation, the MpCN algorithm becomes a random-walk Metropolis algorithm.

Keywords

Markov chainergodicityMonte Carloregular variation

MSC classification

Primary: 65C05: Monte Carlo methods
Secondary: 65C40: Computational Markov chains 60J05: Discrete-time Markov processes on general state spaces
Type
Research Papers
Information
Journal of Applied Probability , Volume 54 , Issue 2 , June 2017 , pp. 638 - 654
Copyright
Copyright © Applied Probability Trust 2017 

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