Journal
ANNALS OF APPLIED PROBABILITY
Volume 19, Issue 3, Pages 863-898Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/08-AAP563
Keywords
Random-walk metropolis; Langevin; squared-jump-distance; Gaussian law on Hilbert space; Karhunen-Loeve; Navier-Stokes PDE; diffusion
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Funding
- EPSRC
- Engineering and Physical Sciences Research Council [EP/D00375X/1, EP/D002060/1] Funding Source: researchfish
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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 -> infinity. 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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