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.
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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 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 |
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