SPDE limits of the random walk Metropolis algorithm in high dimensions
Mattingly, Jonathan C., Pillai, Natesh S., 1981- and Stuart, A. M. (2009) SPDE limits of the random walk Metropolis algorithm in high dimensions. Working Paper. University of Warwick. Centre for Research in Statistical Methodology, Coventry.
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Diffusion limits of MCMC methods in high dimensions provide a useful theoretical tool for studying efficiency. In particular they facilitate 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 only been proved for target measures with a product structure, severely limiting their applicability to real applications. The purpose of this paper is to study diffusion limits for a class of naturally occuring 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 to an infinite dimensional Hilbert space valued SDE (or SPDE) is proved.
|Item Type:||Working or Discussion Paper (Working Paper)|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of Science > Mathematics
Faculty of Science > Statistics
|Library of Congress Subject Headings (LCSH):||Random walks (Mathematics), Monte Carlo method, Markov processes, Sampling (Statistics)|
|Series Name:||Working papers|
|Publisher:||University of Warwick. Centre for Research in Statistical Methodology|
|Place of Publication:||Coventry|
|Number of Pages:||42|
|Status:||Not Peer Reviewed|
|Access rights to Published version:||Open Access|
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