Perturbation bounds for Monte Carlo within Metropolis via restricted approximations

Felipe Medina-Aguayo, Daniel Rudolf, Nikolaus Schweizer

Research output: Contribution to journalArticleScientificpeer-review

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 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.
Original languageEnglish
JournalStochastic Processes and their Applications
DOIs
Publication statusE-pub ahead of print - 26 Jun 2019

Fingerprint

Perturbation Bound
Markov processes
Markov chain
Approximation
Metropolis-Hastings
Metropolis Algorithm
Metropolis-Hastings Algorithm
Monte Carlo Algorithm
Sampling
Transition Probability
Verify
Perturbation
Target
Estimate

Keywords

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

Cite this

@article{d66c4429872f4cc0a9efed8a9fc3e968,
title = "Perturbation bounds for Monte Carlo within Metropolis via restricted approximations",
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 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",
author = "Felipe Medina-Aguayo and Daniel Rudolf and Nikolaus Schweizer",
year = "2019",
month = "6",
day = "26",
doi = "10.1016/j.spa.2019.06.015",
language = "English",
journal = "Stochastic Processes and their Applications",
issn = "0304-4149",
publisher = "Elsevier",

}

Perturbation bounds for Monte Carlo within Metropolis via restricted approximations. / Medina-Aguayo, Felipe; Rudolf, Daniel; Schweizer, Nikolaus.

In: Stochastic Processes and their Applications, 26.06.2019.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Perturbation bounds for Monte Carlo within Metropolis via restricted approximations

AU - Medina-Aguayo, Felipe

AU - Rudolf, Daniel

AU - Schweizer, Nikolaus

PY - 2019/6/26

Y1 - 2019/6/26

N2 - 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 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.

AB - 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 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.

KW - Markov chain Monte Carlo

KW - restricted approximation

KW - Monte Carlo within Metropolis

KW - intractable likelihood

U2 - 10.1016/j.spa.2019.06.015

DO - 10.1016/j.spa.2019.06.015

M3 - Article

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

SN - 0304-4149

ER -