Beskos, Alexandros, Roberts, Gareth O. and Stuart, A. M. (2009) Optimal scalings for local Metropolis–Hastings chains on nonproduct targets in high dimensions. Annals of Applied Probability, Vol.19 (No.3). pp. 863-898. doi:10.1214/08-AAP563 ISSN 1050-5164.

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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:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Journal or Publication Title:	Annals of Applied Probability
Publisher:	Institute of Mathematical Statistics
ISSN:	1050-5164
Official Date:	June 2009
Dates:	Date Event June 2009 Published
Volume:	Vol.19
Number:	No.3
Page Range:	pp. 863-898
DOI:	10.1214/08-AAP563
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access

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