Convergence of adaptive mixtures of importance sampling schemes

Details Convergence of adaptive mixtures of importance sampling schemes Convergence of adaptive mixtures of importance sampling schemes

2007-08-06

arxiv.org/abs/0708.0711v1

Annals of Statistics (2007), Vol. 35, No. 1, 420-448

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053606000001154 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053606000001154

In the design of efficient simulation algorithms, one is often beset with a poor choice of proposal distributions. Although the performance of a given simulation kernel can clarify a posteriori how adequate this kernel is for the problem at hand, a permanent on-line modification of kernels causes concerns about the validity of the resulting algorithm. While the issue is most often intractable for MCMC algorithms, the equivalent version for importance sampling algorithms can be validated quite precisely. We derive sufficient convergence conditions for adaptive mixtures of population Monte Carlo algorithms and show that Rao--Blackwellized versions asymptotically achieve an optimum in terms of a Kullback divergence criterion, while more rudimentary versions do not benefit from repeated updating.

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