Betancourt, M;
Byrne, S;
Livingstone, S;
Girolami, M;
(2017)
The geometric foundations of Hamiltonian Monte Carlo.
Bernoulli
, 23
(4A)
pp. 2257-2298.
10.3150/16-BEJ810.
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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.
| Type: | Article |
|---|---|
| Title: | The geometric foundations of Hamiltonian Monte Carlo |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.3150/16-BEJ810 |
| Publisher version: | https://doi.org/10.3150/16-BEJ810 |
| Language: | English |
| Additional information: | This is the published version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | differential geometry; disintegration; fiber bundle; Hamiltonian Monte Carlo; Markov chain Monte Carlo; Riemannian geometry; symplectic geometry; smooth manifold |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1457094 |
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