Beskos, Alexandros and Roberts, Gareth and Stuart, Andrew (2009) Optimal scalings for local Metropolis–Hastings chains on nonproduct targets in high dimensions. Annals of Applied Probability, 19 (3). pp. 863-898. ISSN 1050-5164. https://resolver.caltech.edu/CaltechAUTHORS:20160805-153017689
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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.
Item Type: | Article | ||||||||||||
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Additional Information: | © 2009 Institute of Mathematical Statistics. Received July 2008; revised September 2008. Supported by an EPSRC grant. | ||||||||||||
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Subject Keywords: | Random-walk metropolis, Langevin, squared-jump-distance, Gaussian law on Hilbert space, Karhunen–Loève, Navier–Stokes PDE, diffusion. | ||||||||||||
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Issue or Number: | 3 | ||||||||||||
Classification Code: | AMS 2000 subject classifications. Primary 60J22; secondary 65C40 | ||||||||||||
Record Number: | CaltechAUTHORS:20160805-153017689 | ||||||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20160805-153017689 | ||||||||||||
Official Citation: | 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. http://projecteuclid.org/euclid.aoap/1245071013. | ||||||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||
ID Code: | 69485 | ||||||||||||
Collection: | CaltechAUTHORS | ||||||||||||
Deposited By: | Linda Taddeo | ||||||||||||
Deposited On: | 05 Aug 2016 23:45 | ||||||||||||
Last Modified: | 03 Oct 2019 10:22 |
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