Improving the Asymptotic Performance of Markov Chain Monte-Carlo by Inserting Vortices

2012/09/26 by Yi Sun, Faustino Gomez, Sun, Yi +3
Mathematics · #FOS: Computer and information sciences #Methodology (stat.ME) #stat.ME

paper · pdf · doi:10.48550/arxiv.1209.6048

Published in NIPS 2010

arxiv created 2012/09/26 · arxiv updated 2012/09/27

Abstract

We present a new way of converting a reversible finite Markov chain into a non-reversible one, with a theoretical guarantee that the asymptotic variance of the MCMC estimator based on the non-reversible chain is reduced. The method is applicable to any reversible chain whose states are not connected through a tree, and can be interpreted graphically as inserting vortices into the state transition graph. Our result confirms that non-reversible chains are fundamentally better than reversible ones in terms of asymptotic performance, and suggests interesting directions for further improving MCMC.

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