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SPDE limits of the random walk Metropolis algorithm in high dimensions
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Mattingly, Jonathan C., Pillai, Natesh S. and Stuart, A. M. (2009) SPDE limits of the random walk Metropolis algorithm in high dimensions. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. Working papers, Vol.2009 (No.19).

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Official URL: http://www2.warwick.ac.uk/fac/sci/statistics/crism...
Abstract
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 
Official Date:  2009 
Volume:  Vol.2009 
Number:  No.19 
Number of Pages:  42 
Status:  Not Peer Reviewed 
Access rights to Published version:  Open Access 
References:  B´edard, Myl`ene. 2007. Weak convergence of Metropolis algorithms for noni.i.d. target 
URI:  http://wrap.warwick.ac.uk/id/eprint/35206 
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