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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., 1981 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).

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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 
Date:  2009 
Volume:  Vol.2009 
Number:  No.19 
Number of Pages:  42 
Status:  Not Peer Reviewed 
Access rights to Published version:  Open Access 
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URI:  http://wrap.warwick.ac.uk/id/eprint/35206 
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