Barp, A;
Briol, FX;
Kennedy, AD;
Girolami, M;
(2018)
Geometry and Dynamics for Markov Chain Monte Carlo.
Annual Review of Statistics and Its Application
, 5
pp. 451-471.
10.1146/annurev-statistics-031017-100141.
Text
Briol_Geometry and Dynamics for Markov Chain Monte Carlo_AAM.pdf - Accepted Version Access restricted to UCL open access staff Download (1MB) |
Abstract
Markov chain Monte Carlo methods have revolutionized mathematical computation and enabled statistical inference within many previously intractable models. In this context, Hamiltonian dynamics have been proposed as an efficient way of building chains that can explore probability densities efficiently. The method emerges from physics and geometry, and these links have been extensively studied over the past thirty years. The aim of this review is to provide a comprehensive introduction to the geometric tools used in Hamiltonian Monte Carlo at a level accessible to statisticians, machine learners, and other users of the methodology with only a basic understanding of Monte Carlo methods. This will be complemented with some discussion of the most recent advances in the field, which we believe will become increasingly relevant to scientists.
Type: | Article |
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Title: | Geometry and Dynamics for Markov Chain Monte Carlo |
DOI: | 10.1146/annurev-statistics-031017-100141 |
Publisher version: | https://doi.org/10.1146/annurev-statistics-031017-... |
Language: | English |
Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
Keywords: | Markov chain Monte Carlo, information geometry, Hamiltonian mechanics, symplectic integrators, shadow Hamiltonians |
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/10079216 |
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