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On the containment condition for adaptive Markov Chain Monte Carlo algorithms
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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. Coventry: University of Warwick. Centre for Research in Statistical Methodology. Working papers, Vol.2009 (No.15).
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Official URL: http://www2.warwick.ac.uk/fac/sci/statistics/crism...
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) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > 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 | ||||
Official Date: | 2009 | ||||
Dates: |
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Volume: | Vol.2009 | ||||
Number: | No.15 | ||||
Number of Pages: | 25 | ||||
Institution: | University of Warwick | ||||
Status: | Not Peer Reviewed | ||||
Access rights to Published version: | Open Access (Creative Commons) | ||||
Date of first compliant deposit: | 1 August 2016 | ||||
Date of first compliant Open Access: | 1 August 2016 | ||||
Funder: | Natural Sciences and Engineering Research Council of Canada (NSERC) |
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