Mattingly, Jonathan C. and Pillai, Natesh S. and Stuart, Andrew M. (2012) Diffusion limits of the random walk Metropolis algorithm in high dimensions. Annals of Applied Probability, 22 (3). pp. 881-930. ISSN 1050-5164. doi:10.1214/10-AAP754. https://resolver.caltech.edu/CaltechAUTHORS:20160728-154635836
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Abstract
Diffusion limits of MCMC methods in high dimensions provide a useful theoretical tool for studying computational complexity. In particular, they lead directly to 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 mainly been proved for target measures with a product structure, severely limiting their applicability. The purpose of this paper is to study diffusion limits for a class of naturally occurring 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 of a random walk Metropolis algorithm to an infinite-dimensional Hilbert space valued SDE (or SPDE) is proved, facilitating understanding of the computational complexity of the algorithm.
Item Type: | Article | ||||||||||||
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Additional Information: | © Institute of Mathematical Statistics, 2012. Received March 2010; revised November 2010. [JCM] Supported by NSF Grants DMS-04-49910 and DMS-08-54879. [AMS] Supported by EPSRC and ERC. | ||||||||||||
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Subject Keywords: | Markov chain Monte Carlo, scaling limits, optimal convergence time, stochastic PDEs. | ||||||||||||
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Issue or Number: | 3 | ||||||||||||
Classification Code: | MSC2010 subject classifications. 60J22, 60H15, 65C05, 65C40, 60J20. | ||||||||||||
DOI: | 10.1214/10-AAP754 | ||||||||||||
Record Number: | CaltechAUTHORS:20160728-154635836 | ||||||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20160728-154635836 | ||||||||||||
Official Citation: | Mattingly, Jonathan C.; Pillai, Natesh S.; Stuart, Andrew M. Diffusion limits of the random walk Metropolis algorithm in high dimensions. Ann. Appl. Probab. 22 (2012), no. 3, 881--930. doi:10.1214/10-AAP754. http://projecteuclid.org/euclid.aoap/1337347534. | ||||||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||
ID Code: | 69294 | ||||||||||||
Collection: | CaltechAUTHORS | ||||||||||||
Deposited By: | Linda Taddeo | ||||||||||||
Deposited On: | 01 Aug 2016 22:23 | ||||||||||||
Last Modified: | 11 Nov 2021 04:12 |
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