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Paper No. 14-13

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RV Craiu, G Lawrence, K Latuszynski, N Madras, GO Roberts and JS Rosenthal

Stability of Adversarial Markov Chains, with an Application to Adaptive MCMC Algorithms

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