Diffusion limits of the random walk Metropolis algorithm in high dimensions

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 st...

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Vydáno v:arXiv.org
Hlavní autoři: Mattingly, Jonathan C, Pillai, Natesh S, Stuart, Andrew M
Médium: Paper
Jazyk:angličtina
Vydáno: Ithaca Cornell University Library, arXiv.org 04.10.2012
Témata:
Algorithms
Complexity
Computation
Diffusion
Hilbert space
Random walk
Software
ISSN:2331-8422
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Shrnutí: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.
Bibliografie:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
content type line 50
ISSN:2331-8422
DOI:10.48550/arxiv.1003.4306