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Perturbation bounds for Monte Carlo within metropolis via restricted approximations

Medina-Aguayo, F., Rudolf, D. and Schweizer, N. (2020) Perturbation bounds for Monte Carlo within metropolis via restricted approximations. Stochastic Processes and their Applications, 130 (4). pp. 2200-2227. ISSN 0304-4149

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To link to this item DOI: 10.1016/j.spa.2019.06.015

Abstract/Summary

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 n-th 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. Keywords: Markov chain Monte Carlo, restricted approximation, Monte Carlo within Metropolis, intractable likelihood.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:84443
Publisher:Elsevier

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