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Non-reversible Metropolis-Hastings
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Bierkens, Joris (2016) Non-reversible Metropolis-Hastings. Statistics and Computing, 26 (6). pp. 1213-1228. doi:10.1007/s11222-015-9598-x ISSN 0960-3174.
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Official URL: http://dx.doi.org/10.1007/s11222-015-9598-x
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 | ||||||||||
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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: |
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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 (Creative Commons) | ||||||||||
Date of first compliant deposit: | 16 March 2016 | ||||||||||
Date of first compliant Open Access: | 16 March 2016 |
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