Open Access
November 2017 The geometric foundations of Hamiltonian Monte Carlo
Michael Betancourt, Simon Byrne, Sam Livingstone, Mark Girolami
Bernoulli 23(4A): 2257-2298 (November 2017). DOI: 10.3150/16-BEJ810


Although Hamiltonian Monte Carlo has proven an empirical success, the lack of a rigorous theoretical understanding of the algorithm has in many ways impeded both principled developments of the method and use of the algorithm in practice. In this paper, we develop the formal foundations of the algorithm through the construction of measures on smooth manifolds, and demonstrate how the theory naturally identifies efficient implementations and motivates promising generalizations.


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Michael Betancourt. Simon Byrne. Sam Livingstone. Mark Girolami. "The geometric foundations of Hamiltonian Monte Carlo." Bernoulli 23 (4A) 2257 - 2298, November 2017.


Received: 1 May 2015; Published: November 2017
First available in Project Euclid: 9 May 2017

zbMATH: 1380.60070
MathSciNet: MR3648031
Digital Object Identifier: 10.3150/16-BEJ810

Keywords: Differential geometry , disintegration , fiber bundle , Hamiltonian Monte Carlo , Markov chain Monte Carlo , Riemannian geometry , smooth manifold , symplectic geometry

Rights: Copyright © 2017 Bernoulli Society for Mathematical Statistics and Probability

Vol.23 • No. 4A • November 2017
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