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The geometric foundations of Hamiltonian Monte Carlo
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Betancourt, Michael, Byrne, Simon, Livingstone, Sam and Girolami, Mark (2017) The geometric foundations of Hamiltonian Monte Carlo. Bernoulli, 23 (4A). pp. 2257-2298. doi:10.3150/16-BEJ810
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Official URL: https://doi.org/10.3150/16-BEJ810
Abstract
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.
| Item Type: | Journal Article | ||||||
|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software | ||||||
| Divisions: | Faculty of Science > Statistics | ||||||
| Library of Congress Subject Headings (LCSH): | Markov processes, Hamiltonian systems, Geometry, Differential, Geometry, Riemannian, Symplectic geometry | ||||||
| Journal or Publication Title: | Bernoulli | ||||||
| Publisher: | Int Statistical Institute | ||||||
| ISSN: | 1350-7265 | ||||||
| Official Date: | 9 May 2017 | ||||||
| Dates: |
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| Volume: | 23 | ||||||
| Number: | 4A | ||||||
| Page Range: | pp. 2257-2298 | ||||||
| DOI: | 10.3150/16-BEJ810 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Open Access | ||||||
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