Convergence of Adaptive Sampling Schemes

Randal Douc, Arnaud Guillin, Jean-Michel Marin and Christian P, Robert
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Randal Douc: Crest
Arnaud Guillin: Crest
Jean-Michel Marin: Crest
Christian P, Robert: Crest

No 2004-45, Working Papers from Center for Research in Economics and Statistics

Abstract: In the design of effcient simulation algorithms, one is often beset with a poorchoice of proposal distributions. Although the performances of a given kernel canclarify how adequate it is for the problem at hand, a permanent on-line modi cationof kernels causes concerns about the validity of the resulting algorithm. While theissue is quite complex and most often intractable for MCMC algorithms, the equivalentversion for importance sampling algorithms can be validated quite precisely.We derive suffcient convergence conditions for a wide class of population MonteCarlo algorithms and show that Rao{Blackwellized versions asymptotically achievean optimum in terms of a Kullback divergence criterion, while more rudimentaryversions simply do not bene t from repeated updating. Adaptivity, Bayesian Statistics, CLT, importance sampling, Kullbackdivergence, LLN, MCMC algorithm, population Monte Carlo, Rao-Blackwellization.

Date: 2004
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