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arXiv · 1601.00225

Identifying the Optimal Integration Time in Hamiltonian Monte Carlo

Michael Betancourt
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Abstract

By leveraging the natural geometry of a smooth probabilistic system, Hamiltonian Monte Carlo yields computationally efficient Markov Chain Monte Carlo estimation. At least provided that the algorithm is sufficiently well-tuned. In this paper I show how the geometric foundations of Hamiltonian Monte Carlo implicitly identify the optimal choice of these parameters, especially the integration time. I then consider the practical consequences of these principles in both existing algorithms and a new implementation called \emph{Exhaustive Hamiltonian Monte Carlo} before demonstrating the utility of these ideas in some illustrative examples.

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Michael Betancourt. 2016-01-02. Identifying the Optimal Integration Time in Hamiltonian Monte Carlo. https://arxiv.org/abs/1601.00225

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