Bierkens, Joris (2016) Non-reversible Metropolis-Hastings. Statistics and Computing, 26 (6). pp. 1213-1228. doi:10.1007/s11222-015-9598-x

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Abstract

The classical Metropolis-Hastings (MH) algorithm can be extended to generate non-reversible Markov chains. This is achieved by means of a modification of the acceptance probability, using the notion of vorticity matrix. The resulting Markov chain is non-reversible. Results from the literature on asymptotic variance, large deviations theory and mixing time are mentioned, and in the case of a large deviations result, adapted, to explain how non-reversible Markov chains have favorable properties in these respects. We provide an application of NRMH in a continuous setting by developing the necessary theory and applying, as first examples, the theory to Gaussian distributions in three and nine dimensions. The empirical autocorrelation and estimated asymptotic variance for NRMH applied to these examples show significant improvement compared to MH with identical stepsize.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Statistics
Library of Congress Subject Headings (LCSH):	Markov processes, Monte Carlo method
Journal or Publication Title:	Statistics and Computing
Publisher:	Springer
ISSN:	0960-3174
Official Date:	November 2016
Dates:	Date Event November 2016 Published 18 August 2015 Available 23 July 2015 Accepted 12 March 2015 Submitted
Volume:	26
Number:	6
Number of Pages:	16
Page Range:	pp. 1213-1228
DOI:	10.1007/s11222-015-9598-x
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access

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