The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 25, Number 6 (2015), 3592-3623.
Stability of adversarial Markov chains, with an application to adaptive MCMC algorithms
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.
Ann. Appl. Probab., Volume 25, Number 6 (2015), 3592-3623.
Received: March 2014
Revised: August 2014
First available in Project Euclid: 1 October 2015
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60J05: Discrete-time Markov processes on general state spaces
Secondary: 60J22: Computational methods in Markov chains [See also 65C40] 62F10: Point estimation 62F15: Bayesian inference
Craiu, Radu V.; Gray, Lawrence; Łatuszyński, Krzysztof; Madras, Neal; Roberts, Gareth O.; Rosenthal, Jeffrey S. Stability of adversarial Markov chains, with an application to adaptive MCMC algorithms. Ann. Appl. Probab. 25 (2015), no. 6, 3592--3623. doi:10.1214/14-AAP1083. https://projecteuclid.org/euclid.aoap/1443703783