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

Ludkin, Matthew and Sherlock, Chris (2022) Hug and Hop:a discrete-time, nonreversible Markov chain Monte Carlo algorithm. Biometrika. ISSN 0006-3444

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We introduced the Hug and Hop Markov chain Monte Carlo algorithm for estimating expectations with respect to an intractable distribution. The algorithm alternates between two kernels: Hug and Hop. Hug is a non-reversible kernel that repeatedly applies the bounce mechanism from the recently proposed Bouncy Particle Sampler to produce a proposal point 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, however 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.

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This is a pre-copy-editing, author-produced PDF of an article accepted for publication in British Journal for the Philosophy of Science following peer review. The definitive publisher-authenticated version M Ludkin, C Sherlock, Hug and Hop: a discrete-time, nonreversible Markov chain Monte Carlo algorithm, Biometrika, 2022;, asac039 is available online at:
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12 Jul 2022 15:35
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13 Sep 2022 13:35