The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 19, Number 3 (2009), 863-898.
Optimal scalings for local Metropolis–Hastings chains on nonproduct targets in high dimensions
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.
Ann. Appl. Probab., Volume 19, Number 3 (2009), 863-898.
First available in Project Euclid: 15 June 2009
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60J22: Computational methods in Markov chains [See also 65C40]
Secondary: 65C40: Computational Markov chains
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. https://projecteuclid.org/euclid.aoap/1245071013