STABILITY OF ADVERSARIAL MARKOV CHAINS, WITH AN APPLICATION TO ADAPTIVE MCMC ALGORITHMS

• 成果类型: Article
• 署名作者: Craiu, Radu V.; Gray, Lawrence; Latuszynski, Krzysztof; Madras, Neal; Roberts, Gareth O.; Rosenthal, Jeffrey S.
• 署名单位: University of Toronto; University of Minnesota System; University of Minnesota Twin Cities; University of Warwick; York University - Canada
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/14-AAP1083
• 发表日期: 2015
• 页码: 3592-3623
• 关键词: Ergodicity; drift

摘要

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.