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Hug and hop: a discrete-time, nonreversible Markov chain Monte Carlo algorithm

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  • M Ludkin
  • C Sherlock

Abstract

SummaryThis article introduces the hug and hop Markov chain Monte Carlo algorithm for estimating expectations with respect to an intractable distribution. The algorithm alternates between two kernels, referred to as hug and hop. Hug is a nonreversible kernel that repeatedly applies the bounce mechanism from the recently proposed bouncy particle sampler to produce a proposal point that is far from the current position yet on almost the same contour of the target density, leading to a high acceptance probability. Hug is complemented by hop, which deliberately proposes jumps between contours and has an efficiency that degrades very slowly with increasing dimension. There are many parallels between hug and Hamiltonian Monte Carlo using a leapfrog integrator, including the order of the integration scheme, but hug is also able to make use of local Hessian information without requiring implicit numerical integration steps, and its performance is not terminally affected by unbounded gradients of the log-posterior. We test hug and hop empirically on a variety of toy targets and real statistical models, and find that it can, and often does, outperform Hamiltonian Monte Carlo.

Suggested Citation

  • M Ludkin & C Sherlock, 2023. "Hug and hop: a discrete-time, nonreversible Markov chain Monte Carlo algorithm," Biometrika, Biometrika Trust, vol. 110(2), pages 301-318.
    • Handle: RePEc:oup:biomet:v:110:y:2023:i:2:p:301-318.
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    File URL: http://hdl.handle.net/10.1093/biomet/asac039
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    References listed on IDEAS

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    1. C Sherlock & A H Thiery, 2022. "A discrete bouncy particle sampler [Hypocoercivity of piecewise deterministic Markov process-Monte Carlo]," Biometrika, Biometrika Trust, vol. 109(2), pages 335-349.
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    3. Bierkens, Joris & Bouchard-Côté, Alexandre & Doucet, Arnaud & Duncan, Andrew B. & Fearnhead, Paul & Lienart, Thibaut & Roberts, Gareth & Vollmer, Sebastian J., 2018. "Piecewise deterministic Markov processes for scalable Monte Carlo on restricted domains," Statistics & Probability Letters, Elsevier, vol. 136(C), pages 148-154.
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