Kinetic energy choice in Hamiltonian/hybrid Monte Carlo

S Livingstone, M F Faulkner and G O Roberts

Biometrika, 2019, vol. 106, issue 2, 303-319

Abstract: SummaryWe 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.

Keywords: Bayesian computation; Bayesian inference; Hamiltonian Monte Carlo; Hybrid Monte Carlo; Markov chain Monte Carlo (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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