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