Bai, Yan, Roberts, Gareth O. and Rosenthal, Jeffrey S. (Jeffrey Seth) (2009) On the containment condition for adaptive Markov Chain Monte Carlo algorithms. Working Paper. University of Warwick. Centre for Research in Statistical Methodology, Coventry.

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Abstract

This paper considers ergodicity properties of certain adaptive Markov chain Monte Carlo (MCMC) algorithms for multidimensional target distributions, in particular Adaptive Metropolis and Adaptive Metropolis-within-Gibbs. It was previously shown (Roberts and Rosenthal [21]) that Diminishing Adaptation and Containment imply ergodicity of adaptive MCMC. We derive various sufficient conditions to ensure Containment, and connect the convergence rates of algorithms with the tail properties of the corresponding target distributions. An example is given to show that Diminishing Adaptation alone does not imply ergodicity. We also present a Summable Adaptive Condition which, when satisfied, proves ergodicity more easily.

Item Type:	Working or Discussion Paper (Working Paper)
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH):	Markov processes, Monte Carlo method, Ergodic theory
Series Name:	Working papers
Publisher:	University of Warwick. Centre for Research in Statistical Methodology
Place of Publication:	Coventry
Date:	2009
Volume:	Vol.2009
Number:	No.15
Number of Pages:	25
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access
Funder:	Natural Sciences and Engineering Research Council of Canada (NSERC)
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URI:	http://wrap.warwick.ac.uk/id/eprint/35203

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