Kinetic energy choice in Hamiltonian/hybrid Monte Carlo
成果类型：
Article
署名作者：
Livingstone, S.; Faulkner, M. F.; Roberts, G. O.
署名单位：
University of Bristol; University of Warwick
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.1093/biomet/asz013
发表日期：
2019
页码：
303319
关键词：
摘要：
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.
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