Date
2007
Dewey
Probabilités et mathématiques appliquées
Sujet
Bayesian statistics; LLN; Kullback divergence; MCMC algorithm; population Monte Carlo; proposal distribution; Rao–Blackwellization
Journal issue
Annals of Statistics
Volume
35
Number
1
Publication date
2007
Article pages
420-448
Publisher
Institute of Mathematical Statistics
Author
Douc, Randal
Guillin, Arnaud
Marin, Jean-Michel
Robert, Christian P.
Type
Article accepté pour publication ou publié
Abstract (EN)
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.