Persistent Link:
http://hdl.handle.net/10150/244823
Title:
Markov Chain Monte Carlo and Non-Reversible Methods
Author:
Xu, Jason Qian
Issue Date:
May-2012
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
The bulk of Markov chain Monte Carlo applications make use of reversible chains, relying on the Metropolis-Hastings algorithm or similar methods. While reversible chains have the advantage of being relatively easy to analyze, it has been shown that non-reversible chains may outperform them in various scenarios. Neal proposes an algorithm that transforms a general reversible chain into a non-reversible chain with a construction that does not increase the asymptotic variance. These modified chains work to avoid diffusive backtracking behavior which causes Markov chains to be trapped in one position for too long. In this paper, we provide an introduction to MCMC, and discuss the Metropolis algorithm and Neal’s algorithm. We introduce a decaying memory algorithm inspired by Neal’s idea, and then analyze and compare the performance of these chains on several examples.
Type:
text; Electronic Thesis
Degree Name:
B.S.
Degree Level:
bachelors
Degree Program:
Honors College; Mathematics
Degree Grantor:
University of Arizona

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleMarkov Chain Monte Carlo and Non-Reversible Methodsen_US
dc.creatorXu, Jason Qianen_US
dc.contributor.authorXu, Jason Qianen_US
dc.date.issued2012-05-
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractThe bulk of Markov chain Monte Carlo applications make use of reversible chains, relying on the Metropolis-Hastings algorithm or similar methods. While reversible chains have the advantage of being relatively easy to analyze, it has been shown that non-reversible chains may outperform them in various scenarios. Neal proposes an algorithm that transforms a general reversible chain into a non-reversible chain with a construction that does not increase the asymptotic variance. These modified chains work to avoid diffusive backtracking behavior which causes Markov chains to be trapped in one position for too long. In this paper, we provide an introduction to MCMC, and discuss the Metropolis algorithm and Neal’s algorithm. We introduce a decaying memory algorithm inspired by Neal’s idea, and then analyze and compare the performance of these chains on several examples.en_US
dc.typetexten_US
dc.typeElectronic Thesisen_US
thesis.degree.nameB.S.en_US
thesis.degree.levelbachelorsen_US
thesis.degree.disciplineHonors Collegeen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.grantorUniversity of Arizonaen_US
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