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Optimal Scalings for Local Metropolis-hastings Chains on Nonproduct Targets in High Dimensions

Beskos, A; Roberts, G; Stuart, A; (2009) Optimal Scalings for Local Metropolis-hastings Chains on Nonproduct Targets in High Dimensions. The Annals of Applied Probability , 19 (3) 863 - 898. 10.1214/08-AAP563. Green open access

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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.

Type: Article
Title: Optimal Scalings for Local Metropolis-hastings Chains on Nonproduct Targets in High Dimensions
Open access status: An open access version is available from UCL Discovery
DOI: 10.1214/08-AAP563
Publisher version: https://doi.org/10.1214/08-AAP563
Language: English
Additional information: This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Random-walk metropolis, Langevin, squared-jump-distance, Gaussian law on Hilbert space, Karhunen-Loeve, Navier-Stokes PDE, diffusion, ALGORITHMS, DISTRIBUTIONS, DIFFUSIONS
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: https://discovery.ucl.ac.uk/id/eprint/77554
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