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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Hug and Hop
T2 - a discrete-time, nonreversible Markov chain Monte Carlo algorithm
AU - Ludkin, Matthew
AU - Sherlock, Chris
PY - 2023/6/30
Y1 - 2023/6/30
N2 - Summary This 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.
AB - Summary This 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.
U2 - 10.1093/biomet/asac039
DO - 10.1093/biomet/asac039
M3 - Journal article
VL - 110
SP - 301
EP - 318
JO - Biometrika
JF - Biometrika
SN - 0006-3444
IS - 2
ER -