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Convergence of adaptive sampling schemes

R. Douc 1 A. Guillin Jean-Michel Marin 1 C.P. Robert
1 SELECT - Model selection in statistical learning
LMO - Laboratoire de Mathématiques d'Orsay, Inria Saclay - Ile de France
Abstract : In the design of efficient simulation algorithms, one is often beset with a poor choice of proposal distributions. Although the performances of a given kernel can clarify how adequate it 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 quite complex and most often intractable for MCMC algorithms, the equivalent version for importance sampling algorithms can be validated quite precisely. We derive sufficient convergence conditions for a wide class 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 simply do not benefit from repeated updating.
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https://hal.inria.fr/inria-00070522
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Submitted on : Friday, May 19, 2006 - 8:45:42 PM
Last modification on : Wednesday, September 16, 2020 - 5:07:08 PM
Long-term archiving on: : Sunday, April 4, 2010 - 9:24:08 PM

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R. Douc, A. Guillin, Jean-Michel Marin, C.P. Robert. Convergence of adaptive sampling schemes. Annals of Statistics, Institute of Mathematical Statistics, 2007, 35 (1), pp.420-448. ⟨inria-00070522⟩

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