Small-world MCMC and convergence to multi-modal distributions: From slow mixing to fast mixing

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dc.creatorGuan, Yongtao
dc.creatorKrone, Stephen M.
dc.date2007-03-01
dc.date.accessioned2026-07-07T07:49:34Z
dc.date.available2026-07-07T07:49:34Z
dc.descriptionWe compare convergence rates of Metropolis--Hastings chains to multi-modal target distributions when the proposal distributions can be of ``local'' and ``small world'' type. In particular, we show that by adding occasional long-range jumps to a given local proposal distribution, one can turn a chain that is ``slowly mixing'' (in the complexity of the problem) into a chain that is ``rapidly mixing.'' To do this, we obtain spectral gap estimates via a new state decomposition theorem and apply an isoperimetric inequality for log-concave probability measures. We discuss potential applicability of our result to Metropolis-coupled Markov chain Monte Carlo schemes.
dc.descriptionPublished at http://dx.doi.org/10.1214/105051606000000772 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0703021
dc.identifierhttp://arxiv.org/abs/math/0703021
dc.identifierAnnals of Applied Probability 2007, Vol. 17, No. 1, 284-304
dc.identifierdoi:10.1214/105051606000000772
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/124901
dc.subjectProbability
dc.subject65C05 (Primary) 65C40 (Secondary)
dc.titleSmall-world MCMC and convergence to multi-modal distributions: From slow mixing to fast mixing
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