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Quasi-stationary Monte Carlo and the ScaLE Algorithm

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Quasi-stationary Monte Carlo and the ScaLE Algorithm. / Pollock, Murray; Fearnhead, Paul; Johansen, Adam M.; Roberts, Gareth O.

In: Journal of the Royal Statistical Society: Series B (Statistical Methodology), Vol. 82, No. 5, 01.12.2020, p. 1167-1221.

Research output: Contribution to journalJournal articlepeer-review

Harvard

Pollock, M, Fearnhead, P, Johansen, AM & Roberts, GO 2020, 'Quasi-stationary Monte Carlo and the ScaLE Algorithm', Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol. 82, no. 5, pp. 1167-1221. https://doi.org/10.1111/rssb.12365

APA

Pollock, M., Fearnhead, P., Johansen, A. M., & Roberts, G. O. (2020). Quasi-stationary Monte Carlo and the ScaLE Algorithm. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 82(5), 1167-1221. https://doi.org/10.1111/rssb.12365

Vancouver

Pollock M, Fearnhead P, Johansen AM, Roberts GO. Quasi-stationary Monte Carlo and the ScaLE Algorithm. Journal of the Royal Statistical Society: Series B (Statistical Methodology). 2020 Dec 1;82(5):1167-1221. https://doi.org/10.1111/rssb.12365

Author

Pollock, Murray ; Fearnhead, Paul ; Johansen, Adam M. ; Roberts, Gareth O. / Quasi-stationary Monte Carlo and the ScaLE Algorithm. In: Journal of the Royal Statistical Society: Series B (Statistical Methodology). 2020 ; Vol. 82, No. 5. pp. 1167-1221.

Bibtex

@article{47689c5ba6fd4f5791872fcfb15cdb11,
title = "Quasi-stationary Monte Carlo and the ScaLE Algorithm",
abstract = "This paper introduces a class of Monte Carlo algorithms which are based upon simulating 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 whilst retaining exactness: the paper gives theoretical guarantees ensuring the algorithm has the correct limiting target distribution. Furthermore, this methodology is highly amenable to big data problems. By employing a modification to existing naıve sub-sampling and control variate techniques it is possible to obtain an algorithm which is still exact but has sub-linear iterative cost as a function of data size.",
keywords = "stat.ME, stat.CO",
author = "Murray Pollock and Paul Fearnhead and Johansen, {Adam M.} and Roberts, {Gareth O.}",
year = "2020",
month = dec,
day = "1",
doi = "10.1111/rssb.12365",
language = "English",
volume = "82",
pages = "1167--1221",
journal = "Journal of the Royal Statistical Society: Series B (Statistical Methodology)",
issn = "1369-7412",
publisher = "Wiley-Blackwell",
number = "5",

}

RIS

TY - JOUR

T1 - Quasi-stationary Monte Carlo and the ScaLE Algorithm

AU - Pollock, Murray

AU - Fearnhead, Paul

AU - Johansen, Adam M.

AU - Roberts, Gareth O.

PY - 2020/12/1

Y1 - 2020/12/1

N2 - This paper introduces a class of Monte Carlo algorithms which are based upon simulating 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 whilst retaining exactness: the paper gives theoretical guarantees ensuring the algorithm has the correct limiting target distribution. Furthermore, this methodology is highly amenable to big data problems. By employing a modification to existing naıve sub-sampling and control variate techniques it is possible to obtain an algorithm which is still exact but has sub-linear iterative cost as a function of data size.

AB - This paper introduces a class of Monte Carlo algorithms which are based upon simulating 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 whilst retaining exactness: the paper gives theoretical guarantees ensuring the algorithm has the correct limiting target distribution. Furthermore, this methodology is highly amenable to big data problems. By employing a modification to existing naıve sub-sampling and control variate techniques it is possible to obtain an algorithm which is still exact but has sub-linear iterative cost as a function of data size.

KW - stat.ME

KW - stat.CO

U2 - 10.1111/rssb.12365

DO - 10.1111/rssb.12365

M3 - Journal article

VL - 82

SP - 1167

EP - 1221

JO - Journal of the Royal Statistical Society: Series B (Statistical Methodology)

JF - Journal of the Royal Statistical Society: Series B (Statistical Methodology)

SN - 1369-7412

IS - 5

ER -