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Information-Geometric Markov Chain Monte Carlo Methods Using Diffusions

Livingstone, S; Girolami, M; (2014) Information-Geometric Markov Chain Monte Carlo Methods Using Diffusions. Entropy , 16 (6) 3074 - 3102. 10.3390/e16063074. Green open access

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Abstract

Recent work incorporating geometric ideas in Markov chain Monte Carlo is reviewed in order to highlight these advances and their possible application in a range of domains beyond statistics. A full exposition of Markov chains and their use in Monte Carlo simulation for statistical inference and molecular dynamics is provided, with particular emphasis on methods based on Langevin diffusions. After this, geometric concepts in Markov chain Monte Carlo are introduced. A full derivation of the Langevin diffusion on a Riemannian manifold is given, together with a discussion of the appropriate Riemannian metric choice for different problems. A survey of applications is provided, and some open questions are discussed.

Type: Article
Title: Information-Geometric Markov Chain Monte Carlo Methods Using Diffusions
Open access status: An open access version is available from UCL Discovery
DOI: 10.3390/e16063074
Publisher version: http://dx.doi.org/10.3390/e16063074
Language: English
Additional information: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. http://creativecommons.org/licenses/by/3.0/
Keywords: information geometry, Markov chain Monte Carlo, Bayesian inference, computational statistics, machine learning, statistical mechanics, diffusions
UCL classification: UCL
UCL > Provost and Vice Provost Offices
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/1456750
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