The Library
SPDE limits of the random walk Metropolis algorithm in high dimensions
Tools
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, Vol.2009 (No.19).

PDF
WRAP_Mattingly_0919w.pdf  Published Version  Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader Download (806Kb) 
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Status:  Not Peer Reviewed 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 
Request changes or add full text files to a record
Actions (login required)
View Item 
Downloads
Downloads per month over past year