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November 2019 On the geometric ergodicity of Hamiltonian Monte Carlo
Samuel Livingstone, Michael Betancourt, Simon Byrne, Mark Girolami
Bernoulli 25(4A): 3109-3138 (November 2019). DOI: 10.3150/18-BEJ1083

Abstract

We establish general conditions under which Markov chains produced by the Hamiltonian Monte Carlo method will and will not be geometrically ergodic. We consider implementations with both position-independent and position-dependent integration times. In the former case, we find that the conditions for geometric ergodicity are essentially a gradient of the log-density which asymptotically points towards the centre of the space and grows no faster than linearly. In an idealised scenario in which the integration time is allowed to change in different regions of the space, we show that geometric ergodicity can be recovered for a much broader class of tail behaviours, leading to some guidelines for the choice of this free parameter in practice.

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Samuel Livingstone. Michael Betancourt. Simon Byrne. Mark Girolami. "On the geometric ergodicity of Hamiltonian Monte Carlo." Bernoulli 25 (4A) 3109 - 3138, November 2019. https://doi.org/10.3150/18-BEJ1083

Information

Received: 1 November 2017; Revised: 1 September 2018; Published: November 2019
First available in Project Euclid: 13 September 2019

zbMATH: 07110123
MathSciNet: MR4003576
Digital Object Identifier: 10.3150/18-BEJ1083

Rights: Copyright © 2019 Bernoulli Society for Mathematical Statistics and Probability

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Vol.25 • No. 4A • November 2019
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