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Exponential convergence of adaptive importance sampling for Markov chains

Published online by Cambridge University Press:  14 July 2016

Keith Baggerly*
Affiliation:
Rice University
Dennis Cox*
Affiliation:
National Center for Atmospheric Research
Rick Picard*
Affiliation:
Los Alamos National Laboratory
*
Postal address: Department of Statistics, Rice University, 610 South Main St., Houston, TX 77005, USA
∗∗Postal address: Geophysics Statistics project, National Center for Atmospheric Research, PO Box 3000, Boulder, CO 80307-3000, USA. Email address: dcox@cgd.ucar.edu
∗∗∗Postal address: Statistical Sciences Group, MS F600, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

Abstract

We consider adaptive importance sampling for a Markov chain with scoring. It is shown that convergence to the zero-variance importance sampling chain for the mean total score occurs exponentially fast under general conditions. These results extend previous work in Kollman (1993) and in Kollman et al. (1999) for finite state spaces.

MSC classification

Type
Research Papers
Copyright
Copyright © by the Applied Probability Trust 2000 

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Footnotes

This research was supported as part of an ongoing effort to improveMonte Carlo Methods by the Los AlamosNational Laboratory Directed Research and Development Program.

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