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  • PDMP_for_continuous_by_part_densities-6

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PDMP Monte Carlo methods for piecewise-smooth densities

Research output: Contribution to Journal/MagazineJournal article

Forthcoming

Standard

PDMP Monte Carlo methods for piecewise-smooth densities. / Chevallier, Augustin; Power, Sam; Wang, Andi Q. et al.
In: Advances in Applied Probability, 09.11.2023.

Research output: Contribution to Journal/MagazineJournal article

Harvard

Chevallier, A, Power, S, Wang, AQ & Fearnhead, P 2023, 'PDMP Monte Carlo methods for piecewise-smooth densities', Advances in Applied Probability.

APA

Chevallier, A., Power, S., Wang, A. Q., & Fearnhead, P. (in press). PDMP Monte Carlo methods for piecewise-smooth densities. Advances in Applied Probability.

Vancouver

Chevallier A, Power S, Wang AQ, Fearnhead P. PDMP Monte Carlo methods for piecewise-smooth densities. Advances in Applied Probability. 2023 Nov 9.

Author

Chevallier, Augustin ; Power, Sam ; Wang, Andi Q. et al. / PDMP Monte Carlo methods for piecewise-smooth densities. In: Advances in Applied Probability. 2023.

Bibtex

@article{c9448cef04c04f199445ef6e4aab48ee,
title = "PDMP Monte Carlo methods for piecewise-smooth densities",
abstract = " There has been substantial interest in developing Markov chain Monte Carlo algorithms based on piecewise-deterministic Markov processes. However existing algorithms can only be used if the target distribution of interest is differentiable everywhere. The key to adapting these algorithms so that they can sample from to densities with discontinuities is defining appropriate dynamics for the process when it hits a discontinuity. We present a simple condition for the transition of the process at a discontinuity which can be used to extend any existing sampler for smooth densities, and give specific choices for this transition which work with popular algorithms such as the Bouncy Particle Sampler, the Coordinate Sampler and the Zig-Zag Process. Our theoretical results extend and make rigorous arguments that have been presented previously, for instance constructing samplers for continuous densities restricted to a bounded domain, and we present a version of the Zig-Zag Process that can work in such a scenario. Our novel approach to deriving the invariant distribution of a piecewise-deterministic Markov process with boundaries may be of independent interest. ",
keywords = "math.ST, math.PR, stat.CO, stat.ME, stat.TH",
author = "Augustin Chevallier and Sam Power and Wang, {Andi Q.} and Paul Fearnhead",
year = "2023",
month = nov,
day = "9",
language = "English",
journal = "Advances in Applied Probability",
issn = "0001-8678",
publisher = "University of Sheffield",

}

RIS

TY - JOUR

T1 - PDMP Monte Carlo methods for piecewise-smooth densities

AU - Chevallier, Augustin

AU - Power, Sam

AU - Wang, Andi Q.

AU - Fearnhead, Paul

PY - 2023/11/9

Y1 - 2023/11/9

N2 - There has been substantial interest in developing Markov chain Monte Carlo algorithms based on piecewise-deterministic Markov processes. However existing algorithms can only be used if the target distribution of interest is differentiable everywhere. The key to adapting these algorithms so that they can sample from to densities with discontinuities is defining appropriate dynamics for the process when it hits a discontinuity. We present a simple condition for the transition of the process at a discontinuity which can be used to extend any existing sampler for smooth densities, and give specific choices for this transition which work with popular algorithms such as the Bouncy Particle Sampler, the Coordinate Sampler and the Zig-Zag Process. Our theoretical results extend and make rigorous arguments that have been presented previously, for instance constructing samplers for continuous densities restricted to a bounded domain, and we present a version of the Zig-Zag Process that can work in such a scenario. Our novel approach to deriving the invariant distribution of a piecewise-deterministic Markov process with boundaries may be of independent interest.

AB - There has been substantial interest in developing Markov chain Monte Carlo algorithms based on piecewise-deterministic Markov processes. However existing algorithms can only be used if the target distribution of interest is differentiable everywhere. The key to adapting these algorithms so that they can sample from to densities with discontinuities is defining appropriate dynamics for the process when it hits a discontinuity. We present a simple condition for the transition of the process at a discontinuity which can be used to extend any existing sampler for smooth densities, and give specific choices for this transition which work with popular algorithms such as the Bouncy Particle Sampler, the Coordinate Sampler and the Zig-Zag Process. Our theoretical results extend and make rigorous arguments that have been presented previously, for instance constructing samplers for continuous densities restricted to a bounded domain, and we present a version of the Zig-Zag Process that can work in such a scenario. Our novel approach to deriving the invariant distribution of a piecewise-deterministic Markov process with boundaries may be of independent interest.

KW - math.ST

KW - math.PR

KW - stat.CO

KW - stat.ME

KW - stat.TH

M3 - Journal article

JO - Advances in Applied Probability

JF - Advances in Applied Probability

SN - 0001-8678

ER -