Markov Chain Monte Carlo and Non-Reversible Methods
| dc.contributor.author | Xu, Jason Qian | |
| dc.creator | Xu, Jason Qian | en_US |
| dc.date.accessioned | 2012-09-18T22:22:22Z | |
| dc.date.available | 2012-09-18T22:22:22Z | |
| dc.date.issued | 2012-05 | |
| dc.identifier.citation | Xu, Jason Qian. (2012). Markov Chain Monte Carlo and Non-Reversible Methods (Bachelor's thesis, University of Arizona, Tucson, USA). | |
| dc.identifier.uri | http://hdl.handle.net/10150/244823 | |
| dc.description.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. | |
| dc.language.iso | en | en_US |
| dc.publisher | The University of Arizona. | en_US |
| dc.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. | en_US |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | |
| dc.title | Markov Chain Monte Carlo and Non-Reversible Methods | en_US |
| dc.type | text | en_US |
| dc.type | Electronic Thesis | en_US |
| thesis.degree.grantor | University of Arizona | en_US |
| thesis.degree.level | bachelors | en_US |
| thesis.degree.discipline | Honors College | en_US |
| thesis.degree.discipline | Mathematics | en_US |
| thesis.degree.name | B.S. | en_US |
| refterms.dateFOA | 2018-08-26T20:55:57Z | |
| html.description.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. |
