Optimal scalings for local Metropolis–Hastings chains on nonproduct targets in high dimensions
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.
Additional Information
© 2009 Institute of Mathematical Statistics. Received July 2008; revised September 2008. Supported by an EPSRC grant.Attached Files
Published - stuart78.pdf
Submitted - 0908.0865.pdf
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Additional details
- Eprint ID
- 69485
- Resolver ID
- CaltechAUTHORS:20160805-153017689
- Engineering and Physical Sciences Research Council (EPSRC)
- Created
-
2016-08-05Created from EPrint's datestamp field
- Updated
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2021-11-11Created from EPrint's last_modified field
- Other Numbering System Name
- Andrew Stuart
- Other Numbering System Identifier
- J78