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Quasi-stationary Monte Carlo and the ScaLE algorithm

Lookup NU author(s): Professor Murray Pollock

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Abstract

© 2020 The Authors. Journal of the Royal Statistical Society: Series B (Statistical Methodology) Published by John Wiley & Sons Ltd on behalf of Royal Statistical Society.This paper introduces a class of Monte Carlo algorithms which are based on the simulation of a Markov process whose quasi-stationary distribution coincides with a distribution of interest. This differs fundamentally from, say, current Markov chain Monte Carlo methods which simulate a Markov chain whose stationary distribution is the target. We show how to approximate distributions of interest by carefully combining sequential Monte Carlo methods with methodology for the exact simulation of diffusions. The methodology introduced here is particularly promising in that it is applicable to the same class of problems as gradient-based Markov chain Monte Carlo algorithms but entirely circumvents the need to conduct Metropolis–Hastings type accept–reject steps while retaining exactness: the paper gives theoretical guarantees ensuring that the algorithm has the correct limiting target distribution. Furthermore, this methodology is highly amenable to ‘big data’ problems. By employing a modification to existing naive subsampling and control variate techniques it is possible to obtain an algorithm which is still exact but has sublinear iterative cost as a function of data size.

Publication metadata

Author(s): Pollock M, Fearnhead P, Johansen AM, Roberts GO

Publication type: Article

Publication status: Published

Journal: Journal of the Royal Statistical Society. Series B: Statistical Methodology

Year: 2020

Volume: 82

Issue: 5

Pages: 1167-1221

Print publication date: 01/12/2020

Online publication date: 23/10/2020

Acceptance date: 02/04/2016

Date deposited: 09/02/2021

ISSN (print): 1369-7412

ISSN (electronic): 1467-9868

Publisher: Wiley

URL: https://doi.org/10.1111/rssb.12365

DOI: 10.1111/rssb.12365

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