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Stability of adversarial Markov Chains, with an application to adaptive MCMC algorithms
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Craiu, Radu V., Gray, Lawrence F., Łatuszyński, Krzysztof, Madras, Neal Noah, Roberts, Gareth O. and Rosenthal, Jeffrey S. (Jeffrey Seth) (2015) Stability of adversarial Markov Chains, with an application to adaptive MCMC algorithms. The Annals of Applied Probability, 25 (6). pp. 3592-3623. doi:10.1214/14-AAP1083 ISSN 1050-5164.
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Official URL: http://dx.doi.org/10.1214/14-AAP1083
Abstract
We consider whether ergodic Markov chains with bounded step size remain bounded in probability when their transitions are modifed by an adversary on a bounded subset. We provide counterexamples to show that the answer is no in general, and prove theorems to show that the answer is yes under various additional assumptions. We then use our results to prove convergence of various adaptive Markov chain Monte Carlo algorithms.
Item Type: | Journal Article | ||||||||
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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, Ergodic theory, Convergence, Perturbation (Mathematics) | ||||||||
Journal or Publication Title: | The Annals of Applied Probability | ||||||||
Publisher: | Institute of Mathematical Statistics | ||||||||
ISSN: | 1050-5164 | ||||||||
Official Date: | 2015 | ||||||||
Dates: |
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Volume: | 25 | ||||||||
Number: | 6 | ||||||||
Number of Pages: | 32 | ||||||||
Page Range: | pp. 3592-3623 | ||||||||
DOI: | 10.1214/14-AAP1083 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 28 December 2015 | ||||||||
Date of first compliant Open Access: | 28 December 2015 |
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