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December 2015 Stability of adversarial Markov chains, with an application to adaptive MCMC algorithms
Radu V. Craiu, Lawrence Gray, Krzysztof Łatuszyński, Neal Madras, Gareth O. Roberts, Jeffrey S. Rosenthal
Ann. Appl. Probab. 25(6): 3592-3623 (December 2015). DOI: 10.1214/14-AAP1083

Abstract

We consider whether ergodic Markov chains with bounded step size remain bounded in probability when their transitions are modified 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.

Citation

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Radu V. Craiu. Lawrence Gray. Krzysztof Łatuszyński. Neal Madras. Gareth O. Roberts. Jeffrey S. Rosenthal. "Stability of adversarial Markov chains, with an application to adaptive MCMC algorithms." Ann. Appl. Probab. 25 (6) 3592 - 3623, December 2015. https://doi.org/10.1214/14-AAP1083

Information

Received: 1 March 2014; Revised: 1 August 2014; Published: December 2015
First available in Project Euclid: 1 October 2015

zbMATH: 1328.60169
MathSciNet: MR3404645
Digital Object Identifier: 10.1214/14-AAP1083

Subjects:
Primary: 60J05
Secondary: 60J22, 62F10, 62F15

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.25 • No. 6 • December 2015
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