, Volume 18, Issue 4, pp 447-459
Date: 25 Apr 2008

Adaptive importance sampling in general mixture classes

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In this paper, we propose an adaptive algorithm that iteratively updates both the weights and component parameters of a mixture importance sampling density so as to optimise the performance of importance sampling, as measured by an entropy criterion. The method, called M-PMC, is shown to be applicable to a wide class of importance sampling densities, which includes in particular mixtures of multivariate Student t distributions. The performance of the proposed scheme is studied on both artificial and real examples, highlighting in particular the benefit of a novel Rao-Blackwellisation device which can be easily incorporated in the updating scheme.

This work has been supported by the Agence Nationale de la Recherche (ANR) through the 2006–2008 project \(\mathsf{Adap}\) \(\mathsf{MC}\) . Both last authors are grateful to the participants to the BIRS \(\mathsf{07w5079}\) meeting on “Bioinformatics, Genetics and Stochastic Computation: Bridging the Gap”, Banff, for their comments on an earlier version of this paper. The last author also acknowledges an helpful discussion with Geoff McLachlan. The authors wish to thank both referees for their encouraging comments.