Perturbation bounds for Monte Carlo within Metropolis via restricted approximations

Felipe Medina-Aguayo, Daniel Rudolf, Nikolaus Schweizer

Research output: Contribution to journalArticleScientificpeer-review

11 Citations (Scopus)


The Monte Carlo within Metropolis (MCwM) algorithm, interpreted as a perturbed Metropolis–Hastings (MH) algorithm, provides an approach for approximate sampling when the target distribution is intractable. Assuming the unperturbed Markov chain is geometrically ergodic, we show explicit estimates of the difference between the nth step distributions of the perturbed MCwM and the unperturbed MH chains. These bounds are based on novel perturbation results for Markov chains which are of interest beyond the MCwM setting. To apply the bounds, we need to control the difference between the transition probabilities of the two chains and to verify stability of the perturbed chain.

Original languageEnglish
Pages (from-to)2200-2227
Number of pages28
JournalStochastic Processes and their Applications
Issue number4
Publication statusPublished - Apr 2020


  • Markov chain Monte Carlo
  • restricted approximation
  • Monte Carlo within Metropolis
  • intractable likelihood


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