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June 2009 Optimal scalings for local Metropolis–Hastings chains on nonproduct targets in high dimensions
Alexandros Beskos, Gareth Roberts, Andrew Stuart
Ann. Appl. Probab. 19(3): 863-898 (June 2009). DOI: 10.1214/08-AAP563


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.


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Alexandros Beskos. Gareth Roberts. Andrew Stuart. "Optimal scalings for local Metropolis–Hastings chains on nonproduct targets in high dimensions." Ann. Appl. Probab. 19 (3) 863 - 898, June 2009.


Published: June 2009
First available in Project Euclid: 15 June 2009

zbMATH: 1172.60328
MathSciNet: MR2537193
Digital Object Identifier: 10.1214/08-AAP563

Primary: 60J22
Secondary: 65C40

Keywords: diffusion , Gaussian law on Hilbert space , Karhunen–Loève , Langevin , Navier–Stokes PDE , Random-walk metropolis , squared-jump-distance

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.19 • No. 3 • June 2009
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