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    Rights statement: This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Biometrika following peer review. The definitive publisher-authenticated version C Sherlock, A H Thiery, A discrete bouncy particle sampler, Biometrika, Volume 109, Issue 2, June 2022, Pages 335–349 is available online at: https://academic.oup.com/biomet/article/109/2/335/6151695

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A discrete bouncy particle sampler

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A discrete bouncy particle sampler. / Sherlock, Chris; Thiery, Alexandre.

In: Biometrika, Vol. 109, No. 2, 30.06.2022, p. 335-349.

Research output: Contribution to Journal/MagazineJournal articlepeer-review

Harvard

Sherlock, C & Thiery, A 2022, 'A discrete bouncy particle sampler', Biometrika, vol. 109, no. 2, pp. 335-349. https://doi.org/10.1093/biomet/asab013

APA

Vancouver

Sherlock C, Thiery A. A discrete bouncy particle sampler. Biometrika. 2022 Jun 30;109(2):335-349. Epub 2021 Feb 26. doi: 10.1093/biomet/asab013

Author

Sherlock, Chris ; Thiery, Alexandre. / A discrete bouncy particle sampler. In: Biometrika. 2022 ; Vol. 109, No. 2. pp. 335-349.

Bibtex

@article{d9b159f061d04fbfa7680329a2e38b74,
title = "A discrete bouncy particle sampler",
abstract = "Most Markov chain Monte Carlo methods operate in discrete time and are reversible with respect to the target probability. Nevertheless, it is now understood that the use of nonreversible Markov chains can be beneficial in many contexts. In particular, the recently-proposed bouncy particle sampler leverages a continuous-time and nonreversible Markov process and empirically shows state-of-the-art performances when used to explore certain probability densities; however, its implementation typically requires the computation of local upper bounds on the gradient of the log target density. We present the discrete bouncy particle sampler, a general algorithm based upon a guided random walk, a partial refreshment of direction, and a delayed-rejection step. We show that the bouncy particle sampler can be understood as a scaling limit of a special case of our algorithm. In contrast to the bouncy particle sampler, implementing the discrete bouncy particle sampler only requires point-wise evaluation of the target density and its gradient. We propose extensions of the basic algorithm for situations when the exact gradient of the target density is not available. In a Gaussian setting, we establish a scaling limit for the radial process as dimension increases to infinity. We leverage this result to obtain the theoretical efficiency of the discrete bouncy particle sampler as a function of the partial-refreshment parameter, which leads to a simple and robust tuning criterion. A further analysis in a more general setting suggests that this tuning criterion applies more generally. Theoretical and empirical efficiency curves are then compared for different targets and algorithm variations.",
author = "Chris Sherlock and Alexandre Thiery",
note = "This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Biometrika following peer review. The definitive publisher-authenticated version C Sherlock, A H Thiery, A discrete bouncy particle sampler, Biometrika, Volume 109, Issue 2, June 2022, Pages 335–349 is available online at: https://academic.oup.com/biomet/article/109/2/335/6151695",
year = "2022",
month = jun,
day = "30",
doi = "10.1093/biomet/asab013",
language = "English",
volume = "109",
pages = "335--349",
journal = "Biometrika",
issn = "0006-3444",
publisher = "Oxford University Press",
number = "2",

}

RIS

TY - JOUR

T1 - A discrete bouncy particle sampler

AU - Sherlock, Chris

AU - Thiery, Alexandre

N1 - This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Biometrika following peer review. The definitive publisher-authenticated version C Sherlock, A H Thiery, A discrete bouncy particle sampler, Biometrika, Volume 109, Issue 2, June 2022, Pages 335–349 is available online at: https://academic.oup.com/biomet/article/109/2/335/6151695

PY - 2022/6/30

Y1 - 2022/6/30

N2 - Most Markov chain Monte Carlo methods operate in discrete time and are reversible with respect to the target probability. Nevertheless, it is now understood that the use of nonreversible Markov chains can be beneficial in many contexts. In particular, the recently-proposed bouncy particle sampler leverages a continuous-time and nonreversible Markov process and empirically shows state-of-the-art performances when used to explore certain probability densities; however, its implementation typically requires the computation of local upper bounds on the gradient of the log target density. We present the discrete bouncy particle sampler, a general algorithm based upon a guided random walk, a partial refreshment of direction, and a delayed-rejection step. We show that the bouncy particle sampler can be understood as a scaling limit of a special case of our algorithm. In contrast to the bouncy particle sampler, implementing the discrete bouncy particle sampler only requires point-wise evaluation of the target density and its gradient. We propose extensions of the basic algorithm for situations when the exact gradient of the target density is not available. In a Gaussian setting, we establish a scaling limit for the radial process as dimension increases to infinity. We leverage this result to obtain the theoretical efficiency of the discrete bouncy particle sampler as a function of the partial-refreshment parameter, which leads to a simple and robust tuning criterion. A further analysis in a more general setting suggests that this tuning criterion applies more generally. Theoretical and empirical efficiency curves are then compared for different targets and algorithm variations.

AB - Most Markov chain Monte Carlo methods operate in discrete time and are reversible with respect to the target probability. Nevertheless, it is now understood that the use of nonreversible Markov chains can be beneficial in many contexts. In particular, the recently-proposed bouncy particle sampler leverages a continuous-time and nonreversible Markov process and empirically shows state-of-the-art performances when used to explore certain probability densities; however, its implementation typically requires the computation of local upper bounds on the gradient of the log target density. We present the discrete bouncy particle sampler, a general algorithm based upon a guided random walk, a partial refreshment of direction, and a delayed-rejection step. We show that the bouncy particle sampler can be understood as a scaling limit of a special case of our algorithm. In contrast to the bouncy particle sampler, implementing the discrete bouncy particle sampler only requires point-wise evaluation of the target density and its gradient. We propose extensions of the basic algorithm for situations when the exact gradient of the target density is not available. In a Gaussian setting, we establish a scaling limit for the radial process as dimension increases to infinity. We leverage this result to obtain the theoretical efficiency of the discrete bouncy particle sampler as a function of the partial-refreshment parameter, which leads to a simple and robust tuning criterion. A further analysis in a more general setting suggests that this tuning criterion applies more generally. Theoretical and empirical efficiency curves are then compared for different targets and algorithm variations.

U2 - 10.1093/biomet/asab013

DO - 10.1093/biomet/asab013

M3 - Journal article

VL - 109

SP - 335

EP - 349

JO - Biometrika

JF - Biometrika

SN - 0006-3444

IS - 2

ER -