On the containment condition for adaptive Markov Chain Monte Carlo algorithms
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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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 ) 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|
|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|Status:||Not Peer Reviewed|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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