Optimal scaling for partially updating MCMC algorithms

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dc.creatorNeal, Peter
dc.creatorRoberts, Gareth
dc.date2006-07-03
dc.date.accessioned2026-07-07T07:17:56Z
dc.date.available2026-07-07T07:17:56Z
dc.descriptionIn this paper we shall consider optimal scaling problems for high-dimensional Metropolis--Hastings algorithms where updates can be chosen to be lower dimensional than the target density itself. We find that the optimal scaling rule for the Metropolis algorithm, which tunes the overall algorithm acceptance rate to be 0.234, holds for the so-called Metropolis-within-Gibbs algorithm as well. Furthermore, the optimal efficiency obtainable is independent of the dimensionality of the update rule. This has important implications for the MCMC practitioner since high-dimensional updates are generally computationally more demanding, so that lower-dimensional updates are therefore to be preferred. Similar results with rather different conclusions are given for so-called Langevin updates. In this case, it is found that high-dimensional updates are frequently most efficient, even taking into account computing costs.
dc.descriptionPublished at http://dx.doi.org/10.1214/105051605000000791 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/0607054
dc.identifierhttp://arxiv.org/abs/math/0607054
dc.identifierAnnals of Applied Probability 2006, Vol. 16, No. 2, 475-515
dc.identifierdoi:10.1214/105051605000000791
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/114125
dc.subjectProbability
dc.subject60F05 (Primary) 65C05 (Secondary)
dc.titleOptimal scaling for partially updating MCMC algorithms
dc.typetext

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