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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) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics Faculty of Science, Engineering and Medicine > Science > Statistics |
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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 | ||||
Dates: |
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Volume: | Vol.2009 | ||||
Number: | No.19 | ||||
Number of Pages: | 42 | ||||
Status: | Not Peer Reviewed | ||||
Access rights to Published version: | Open Access (Creative Commons) | ||||
Date of first compliant deposit: | 1 August 2016 | ||||
Date of first compliant Open Access: | 1 August 2016 |
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