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Optimal scalings for local Metropolis–Hastings chains on nonproduct targets in high dimensions

Beskos, Alexandros and Roberts, Gareth and Stuart, Andrew (2009) Optimal scalings for local Metropolis–Hastings chains on nonproduct targets in high dimensions. Annals of Applied Probability, 19 (3). pp. 863-898. ISSN 1050-5164. https://resolver.caltech.edu/CaltechAUTHORS:20160805-153017689

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Abstract

We investigate local MCMC algorithms, namely the random-walk Metropolis and the Langevin algorithms, and identify the optimal choice of the local step-size as a function of the dimension n of the state space, asymptotically as n→∞. We consider target distributions defined as a change of measure from a product law. Such structures arise, for instance, in inverse problems or Bayesian contexts when a product prior is combined with the likelihood. We state analytical results on the asymptotic behavior of the algorithms under general conditions on the change of measure. Our theory is motivated by applications on conditioned diffusion processes and inverse problems related to the 2D Navier–Stokes equation.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1214/08-AAP563DOIArticle
http://projecteuclid.org/euclid.aoap/1245071013PublisherArticle
https://arxiv.org/abs/0908.0865arXivDiscussion Paper
Additional Information:© 2009 Institute of Mathematical Statistics. Received July 2008; revised September 2008. Supported by an EPSRC grant.
Funders:
Funding AgencyGrant Number
Engineering and Physical Sciences Research Council (EPSRC)UNSPECIFIED
Subject Keywords:Random-walk metropolis, Langevin, squared-jump-distance, Gaussian law on Hilbert space, Karhunen–Loève, Navier–Stokes PDE, diffusion.
Other Numbering System:
Other Numbering System NameOther Numbering System ID
Andrew StuartJ78
Issue or Number:3
Classification Code:AMS 2000 subject classifications. Primary 60J22; secondary 65C40
Record Number:CaltechAUTHORS:20160805-153017689
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20160805-153017689
Official Citation:Beskos, Alexandros; Roberts, Gareth; Stuart, Andrew. Optimal scalings for local Metropolis–Hastings chains on nonproduct targets in high dimensions. Ann. Appl. Probab. 19 (2009), no. 3, 863--898. doi:10.1214/08-AAP563. http://projecteuclid.org/euclid.aoap/1245071013.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:69485
Collection:CaltechAUTHORS
Deposited By: Linda Taddeo
Deposited On:05 Aug 2016 23:45
Last Modified:03 Oct 2019 10:22

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