Information-Geometric Markov Chain Monte Carlo Methods Using Diffusions

Entropy

Samuel Livingstone¹ 

[1] Department of Statistical Science, University College London, Gower Street, London WC1E 6BT, UK

关键词: information geometry;    Markov chain Monte Carlo;    Bayesian inference;    computational statistics;    machine learning;    statistical mechanics;    diffusions;   

DOI  :  10.3390/e16063074

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2014 by the authors; licensee MDPI, Basel, Switzerland