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Optimal scalings for local Metropolis–Hastings chains on nonproduct targets in high dimensions
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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
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Official URL: http://dx.doi.org/10.1214/08-AAP563
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 > Mathematics | ||||
| Journal or Publication Title: | Annals of Applied Probability | ||||
| Publisher: | Institute of Mathematical Statistics | ||||
| ISSN: | 1050-5164 | ||||
| Official Date: | June 2009 | ||||
| Dates: |
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| 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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