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Kinetic energy choice in Hamiltonian/hybrid Monte Carlo

Author

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  • S Livingstone
  • M F Faulkner
  • G O Roberts

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.

Suggested Citation

  • S Livingstone & M F Faulkner & G O Roberts, 2019. "Kinetic energy choice in Hamiltonian/hybrid Monte Carlo," Biometrika, Biometrika Trust, vol. 106(2), pages 303-319.
    • Handle: RePEc:oup:biomet:v:106:y:2019:i:2:p:303-319.
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    File URL: http://hdl.handle.net/10.1093/biomet/asz013
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    Cited by:

    1. Samuel Livingstone, 2021. "Geometric Ergodicity of the Random Walk Metropolis with Position-Dependent Proposal Covariance," Mathematics, MDPI, vol. 9(4), pages 1-14, February.
    2. Takaaki Koike & Marius Hofert, 2020. "Markov Chain Monte Carlo Methods for Estimating Systemic Risk Allocations," Risks, MDPI, vol. 8(1), pages 1-33, January.

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