A Metropolis-class sampler for targets with non-convex support

John Moriarty; Jure Vogrinc; Alessandro Zocca

doi:10.1007/s11222-021-10044-4

A Metropolis-class sampler for targets with non-convex support

John Moriarty, Jure Vogrinc, Alessandro Zocca^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to Journal › Article › Academic › peer-review

Abstract

We aim to improve upon the exploration of the general-purpose random walk Metropolis algorithm when the target has non-convex support A⊂ R^d, by reusing proposals in A^c which would otherwise be rejected. The algorithm is Metropolis-class and under standard conditions the chain satisfies a strong law of large numbers and central limit theorem. Theoretical and numerical evidence of improved performance relative to random walk Metropolis are provided. Issues of implementation are discussed and numerical examples, including applications to global optimisation and rare event sampling, are presented.

Original language	English
Article number	72
Journal	Statistics and Computing
Volume	31
Issue number	6
DOIs	https://doi.org/10.1007/s11222-021-10044-4
Publication status	Published - Aug 2021

Bibliographical note

Funding Information:
JM was supported by EPSRC grant EP/P002625/1, JV by EPSRC grants EP/N001974/1 and EP/R022100/1, and AZ by NWO Rubicon grant 680.50.1529. The authors wish to thank Wilfrid Kendall, Krzysztof Łatuszyński and Andrew Duncan for useful discussions, and the associate editor and two anonymous referees for their comments which helped improve the manuscript. The authors would like to thank the Isaac Newton Institute for Mathematical Sciences for support and hospitality during the programme “Mathematics of Energy Systems” when work on this paper was undertaken. This work was supported by EPSRC grant number EP/R014604/1.

Publisher Copyright:
© 2021, The Author(s).

Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.

Funding

JM was supported by EPSRC grant EP/P002625/1, JV by EPSRC grants EP/N001974/1 and EP/R022100/1, and AZ by NWO Rubicon grant 680.50.1529. The authors wish to thank Wilfrid Kendall, Krzysztof Łatuszyński and Andrew Duncan for useful discussions, and the associate editor and two anonymous referees for their comments which helped improve the manuscript. The authors would like to thank the Isaac Newton Institute for Mathematical Sciences for support and hospitality during the programme “Mathematics of Energy Systems” when work on this paper was undertaken. This work was supported by EPSRC grant number EP/R014604/1.

Keywords

Global optimisation
Markov Chain Monte Carlo
Metropolis-Hastings algorithm
Multimodal target distribution
Multistart method

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.1007/s11222-021-10044-4

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title = "A Metropolis-class sampler for targets with non-convex support",

abstract = "We aim to improve upon the exploration of the general-purpose random walk Metropolis algorithm when the target has non-convex support A⊂ Rd, by reusing proposals in Ac which would otherwise be rejected. The algorithm is Metropolis-class and under standard conditions the chain satisfies a strong law of large numbers and central limit theorem. Theoretical and numerical evidence of improved performance relative to random walk Metropolis are provided. Issues of implementation are discussed and numerical examples, including applications to global optimisation and rare event sampling, are presented.",

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author = "John Moriarty and Jure Vogrinc and Alessandro Zocca",

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doi = "10.1007/s11222-021-10044-4",

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AB - We aim to improve upon the exploration of the general-purpose random walk Metropolis algorithm when the target has non-convex support A⊂ Rd, by reusing proposals in Ac which would otherwise be rejected. The algorithm is Metropolis-class and under standard conditions the chain satisfies a strong law of large numbers and central limit theorem. Theoretical and numerical evidence of improved performance relative to random walk Metropolis are provided. Issues of implementation are discussed and numerical examples, including applications to global optimisation and rare event sampling, are presented.

KW - Global optimisation

KW - Markov Chain Monte Carlo

KW - Metropolis-Hastings algorithm

KW - Multimodal target distribution

KW - Multistart method

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A Metropolis-class sampler for targets with non-convex support

Abstract

Bibliographical note

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Keywords

UN SDGs

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