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The geometric foundations of Hamiltonian Monte Carlo

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Title: The geometric foundations of Hamiltonian Monte Carlo
Authors: Betancourt, M
Byrne, S
Livingstone, S
Girolami, M
Item Type: Journal Article
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.
Issue Date: 1-Nov-2017
Date of Acceptance: 1-May-2017
URI: http://hdl.handle.net/10044/1/66033
DOI: https://dx.doi.org/10.3150/16-BEJ810
ISSN: 1350-7265
Publisher: Bernoulli Society for Mathematical Statistics and Probability
Start Page: 2257
End Page: 2298
Journal / Book Title: Bernoulli
Volume: 23
Issue: 4A
Copyright Statement: © 2017 ISI/BS.
Keywords: Science & Technology
Physical Sciences
Statistics & Probability
Mathematics
differential geometry
disintegration
fiber bundle
Hamiltonian Monte Carlo
Markov chain Monte Carlo
Riemannian geometry
symplectic geometry
smooth manifold
ALGORITHM
DISINTEGRATION
INFERENCE
SPACES
stat.ME
0104 Statistics
1403 Econometrics
Publication Status: Published
Online Publication Date: 2017-05-09
Appears in Collections:Mathematics
Statistics
Faculty of Natural Sciences



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