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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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Published
<mark>Journal publication date</mark>30/06/2022
<mark>Journal</mark>Biometrika
Issue number2
Volume109
Number of pages15
Pages (from-to)335-349
Publication StatusPublished
Early online date26/02/21
<mark>Original language</mark>English

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.

Bibliographic 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