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Automated State-Dependent Importance Sampling for Markov Jump Processes via Sampling from the Zero-Variance Distribution

Part of: Inference from stochastic processes Markov processes

Published online by Cambridge University Press:  30 January 2018

Adam W. Grace ,
Dirk P. Kroese  and
Werner Sandmann
Adam W. Grace*
Affiliation:
The University of Queensland
Dirk P. Kroese*
Affiliation:
University of Derby
Werner Sandmann*
Affiliation:
University of Derby
*
∗ Postal address: School of Mathematics and Physics, The University of Queensland, Brisbane 4072, QLD, Australia.
∗ Postal address: School of Mathematics and Physics, The University of Queensland, Brisbane 4072, QLD, Australia.
∗∗∗ Postal address: School of Computing and Mathematics, University of Derby, Derby DE22 1GB, UK.
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Abstract

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Many complex systems can be modeled via Markov jump processes. Applications include chemical reactions, population dynamics, and telecommunication networks. Rare-event estimation for such models can be difficult and is often computationally expensive, because typically many (or very long) paths of the Markov jump process need to be simulated in order to observe the rare event. We present a state-dependent importance sampling approach to this problem that is adaptive and uses Markov chain Monte Carlo to sample from the zero-variance importance sampling distribution. The method is applicable to a wide range of Markov jump processes and achieves high accuracy, while requiring only a small sample to obtain the importance parameters. We demonstrate its efficiency through benchmark examples in queueing theory and stochastic chemical kinetics.

Keywords

Importance samplingadaptiveautomatedimproved cross entropystate dependentzero-variance distributionMarkov jump processcontinuous-time Markov chainstochastic chemical kineticsqueueing system

MSC classification

Primary: 60J28: Applications of continuous-time Markov processes on discrete state spaces
Secondary: 62M05: Markov processes
Type
Research Article
Information
Journal of Applied Probability , Volume 51 , Issue 3 , September 2014 , pp. 741 - 755
Copyright
© Applied Probability Trust 

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