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

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)3592-3623
Number of pages32
JournalAnnals of Applied Probability
Volume25
Issue number6
DOIs
StatePublished - Dec 1 2015

Keywords

  • Adaptive MCMC algorithms
  • Convergence
  • Ergodicity
  • Markov chain
  • Perturbation
  • Stability

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