UCL Discovery
UCL home » Library Services » Electronic resources » UCL Discovery

Kinetic energy choice in Hamiltonian/hybrid Monte Carlo

Livingstone, S; Faulkner, MF; Roberts, GO; (2019) Kinetic energy choice in Hamiltonian/hybrid Monte Carlo. Biometrika , 106 (2) pp. 303-319. 10.1093/biomet/asz013. Green open access

[img]
Preview
Text
revision_withoutappendix.pdf - Accepted version

Download (254kB) | Preview
[img]
Preview
Text
revision_suppmaterial.pdf - Accepted version

Download (151kB) | Preview

Abstract

We consider how different choices of kinetic energy in Hamiltonian Monte Carlo affect algorithm performance. To this end, we introduce two quantities which can be easily evaluated, the composite gradient and the implicit noise. Results are established on integrator stability and geometric convergence, and we show that choices of kinetic energy that result in heavy-tailed momentum distributions can exhibit an undesirable negligible moves property, which we define. A general efficiency-robustness trade off is outlined, and implementations which rely on approximate gradients are also discussed. Two numerical studies illustrate our theoretical findings, showing that the standard choice which results in a Gaussian momentum distribution is not always optimal in terms of either robustness or efficiency.

Type: Article
Title: Kinetic energy choice in Hamiltonian/hybrid Monte Carlo
Open access status: An open access version is available from UCL Discovery
DOI: 10.1093/biomet/asz013
Publisher version: https://doi.org/10.1093/biomet/asz013
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Markov chain Monte Carlo; Bayesian Inference; Hamiltonian Monte Carlo; Bayesian computation; Hybrid Monte Carlo; MCMC.
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: https://discovery.ucl.ac.uk/id/eprint/10062156
Downloads since deposit
12Downloads
Download activity - last month
Download activity - last 12 months
Downloads by country - last 12 months

Archive Staff Only

View Item View Item