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Exponential convergence of adaptive importance sampling for Markov chains

Part of: Probabilistic methods, simulation and stochastic differential equations

Published online by Cambridge University Press:  14 July 2016

Keith Baggerly ,
Dennis Cox  and
Rick Picard
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
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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.

Keywords

Adaptive proceduresbiased random walkslearning algorithmsMonte Carlo simulationparticle transportzero-variance solution

MSC classification

Primary: 65C05: Monte Carlo methods
Type
Research Papers
Information
Journal of Applied Probability , Volume 37 , Issue 2 , June 2000 , pp. 342 - 358
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.

References

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