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Diffusion limits of the random walk metropolis algorithm in high dimensions

dc.contributor.author Mattingly, Jonathan Christopher
dc.contributor.author Pillai, NS
dc.contributor.author Stuart, AM
dc.date.accessioned 2015-03-20T17:56:04Z
dc.date.issued 2012-06-01
dc.identifier.issn 1050-5164
dc.identifier.uri https://hdl.handle.net/10161/9523
dc.description.abstract Diffusion limits of MCMC methods in high dimensions provide a useful theoretical tool for studying computational complexity. In particular, they lead directly to precise estimates of the number of steps required to explore the target measure, in stationarity, as a function of the dimension of the state space. However, to date such results have mainly been proved for target measures with a product structure, severely limiting their applicability. The purpose of this paper is to study diffusion limits for a class of naturally occurring high-dimensional measures found from the approximation of measures on a Hilbert space which are absolutely continuous with respect to a Gaussian reference measure. The diffusion limit of a random walk Metropolis algorithm to an infinite-dimensional Hilbert space valued SDE (or SPDE) is proved, facilitating understanding of the computational complexity of the algorithm. © 2012 Institute of Mathematical Statistics.
dc.relation.ispartof Annals of Applied Probability
dc.relation.isversionof 10.1214/10-AAP754
dc.title Diffusion limits of the random walk metropolis algorithm in high dimensions
dc.type Journal article
pubs.begin-page 881
pubs.end-page 890
pubs.issue 3
pubs.organisational-group Duke
pubs.organisational-group Mathematics
pubs.organisational-group Statistical Science
pubs.organisational-group Trinity College of Arts & Sciences
pubs.publication-status Published
pubs.volume 22


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