Perturbation bounds for Monte Carlo within Metropolis via restricted approximations
Medina-Aguayo,Felipe Rudolf,Daniel Schweizer,Nikolaus
Medina-Aguayo,Felipe
Rudolf,Daniel
Schweizer,Nikolaus
Abstract
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.
Description
Publisher Copyright: © 2019 The Authors
Date
2020-04
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Research Projects
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Keywords
Markov chain Monte Carlo, restricted approximation, Monte Carlo within Metropolis, intractable likelihood
Citation
Medina-Aguayo, F, Rudolf, D & Schweizer, N 2020, 'Perturbation bounds for Monte Carlo within Metropolis via restricted approximations', Stochastic Processes and their Applications, vol. 130, no. 4, pp. 2200-2227. https://doi.org/10.1016/j.spa.2019.06.015