A PIECEWISE DETERMINISTIC SCALING LIMIT OF LIFTED METROPOLIS–HASTINGS IN THE CURIE–WEISS MODEL
In Turitsyn, Chertkov and Vucelja [Phys. D 240 (2011) 410-414] a nonreversible Markov Chain Monte Carlo (MCMC) method on an augmented state space was introduced, here referred to as Lifted Metropolis-Hastings (LMH). A scaling limit of the magnetization process in the Curie-Weiss model is derived for...
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| Veröffentlicht in: | The Annals of applied probability 2017-04, Vol.27 (2), p.846-882 |
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| container_title | The Annals of applied probability |
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| creator | Bierkens, Joris Roberts, Gareth |
| description | In Turitsyn, Chertkov and Vucelja [Phys. D 240 (2011) 410-414] a nonreversible Markov Chain Monte Carlo (MCMC) method on an augmented state space was introduced, here referred to as Lifted Metropolis-Hastings (LMH). A scaling limit of the magnetization process in the Curie-Weiss model is derived for LMH, as well as for Metropolis–Hastings (MH). The required jump rate in the high (supercritical) temperature regime equals n½ for LMH, which should be compared to n for MH. At the critical temperature, the required jump rate equals n¾ for LMH and n3/2 for MH, in agreement with experimental results of Turitsyn, Chertkov and Vucelja (2011). The scaling limit of LMH turns out to be a nonreversible piecewise deterministic exponentially ergodic "zig-zag" Markov process. |
| doi_str_mv | 10.1214/16-AAP1217 |
| format | Article |
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D 240 (2011) 410-414] a nonreversible Markov Chain Monte Carlo (MCMC) method on an augmented state space was introduced, here referred to as Lifted Metropolis-Hastings (LMH). A scaling limit of the magnetization process in the Curie-Weiss model is derived for LMH, as well as for Metropolis–Hastings (MH). The required jump rate in the high (supercritical) temperature regime equals n½ for LMH, which should be compared to n for MH. At the critical temperature, the required jump rate equals n¾ for LMH and n3/2 for MH, in agreement with experimental results of Turitsyn, Chertkov and Vucelja (2011). 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D 240 (2011) 410-414] a nonreversible Markov Chain Monte Carlo (MCMC) method on an augmented state space was introduced, here referred to as Lifted Metropolis-Hastings (LMH). A scaling limit of the magnetization process in the Curie-Weiss model is derived for LMH, as well as for Metropolis–Hastings (MH). The required jump rate in the high (supercritical) temperature regime equals n½ for LMH, which should be compared to n for MH. At the critical temperature, the required jump rate equals n¾ for LMH and n3/2 for MH, in agreement with experimental results of Turitsyn, Chertkov and Vucelja (2011). The scaling limit of LMH turns out to be a nonreversible piecewise deterministic exponentially ergodic "zig-zag" Markov process.</description><subject>Computer simulation</subject><subject>Critical temperature</subject><subject>Ergodic processes</subject><subject>Magnetism</subject><subject>Markov analysis</subject><subject>Markov chains</subject><subject>Monte Carlo simulation</subject><subject>Scaling</subject><subject>Temperature</subject><issn>1050-5164</issn><issn>2168-8737</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNptkM1Kw0AUhQdRsFY37oUBcSNE585MMskypNN2ID-lSekyJJkJWNTUpF248x18Q5_EkRbduLqHez7OgYPQNZAHoMAfwXPCcGGlOEEjCp7v-IKJUzQC4hLHBY-fo4th2BBCAh6IEapDvFAykmuVSzyRhVwmKlV5oSKcR2Gs0hmOVaIKnE2tmBZyghNZLLNFFqv86-NzHlo2neVYpbiYSxytlkra_1qqPMdJNpHxJTprq-fBXB3vGK2msojmTpzNlO1wGubSnaM9wQJNA6CMa9O6vtYAtGqhchvCIahEa2oqqqaihhmoqGBGa13XTW15cNkY3R5yt333tjfDrtx0-_7VVpYQMOJ74PvcUvcHqum7YehNW277p5eqfy-BlD8bluCVxw0tfHOAN8Ou639JzikPbKP17_7zbRJlRPxx34F9cuY</recordid><startdate>20170401</startdate><enddate>20170401</enddate><creator>Bierkens, Joris</creator><creator>Roberts, Gareth</creator><general>Institute of Mathematical Statistics</general><scope>AAYXX</scope><scope>CITATION</scope><scope>JQ2</scope></search><sort><creationdate>20170401</creationdate><title>A PIECEWISE DETERMINISTIC SCALING LIMIT OF LIFTED METROPOLIS–HASTINGS IN THE CURIE–WEISS MODEL</title><author>Bierkens, Joris ; Roberts, Gareth</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c352t-d6739d291234def58dd112af1a5c0419a7feb27aca2e3e1a273edddbbcb4de153</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Computer simulation</topic><topic>Critical temperature</topic><topic>Ergodic processes</topic><topic>Magnetism</topic><topic>Markov analysis</topic><topic>Markov chains</topic><topic>Monte Carlo simulation</topic><topic>Scaling</topic><topic>Temperature</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bierkens, Joris</creatorcontrib><creatorcontrib>Roberts, Gareth</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Computer Science Collection</collection><jtitle>The Annals of applied probability</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bierkens, Joris</au><au>Roberts, Gareth</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A PIECEWISE DETERMINISTIC SCALING LIMIT OF LIFTED METROPOLIS–HASTINGS IN THE CURIE–WEISS MODEL</atitle><jtitle>The Annals of applied probability</jtitle><date>2017-04-01</date><risdate>2017</risdate><volume>27</volume><issue>2</issue><spage>846</spage><epage>882</epage><pages>846-882</pages><issn>1050-5164</issn><eissn>2168-8737</eissn><abstract>In Turitsyn, Chertkov and Vucelja [Phys. 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| source | Jstor Complete Legacy; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; Project Euclid Complete; JSTOR Mathematics & Statistics |
| subjects | Computer simulation Critical temperature Ergodic processes Magnetism Markov analysis Markov chains Monte Carlo simulation Scaling Temperature |
| title | A PIECEWISE DETERMINISTIC SCALING LIMIT OF LIFTED METROPOLIS–HASTINGS IN THE CURIE–WEISS MODEL |
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