Jean-Michel Marin

Title: Convergence of adaptive sampling schemes

Abstract:

In the design of efficient simulation algorithms, one is often beset with
a poor choice of proposal distributions. Although the performance of a
given kernel can revelate 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 for
MCMC algorithms, the equivalent version for importance sampling can be
validated quite precisely. We provide sufficient convergence conditions
for a wide class of population Monte Carlo algorithms and show that
Rao--Blackwellised versions asymptotically achieve an optimum in terms of
a Kullback divergence criterion, while more rudimentary versions do not
benefit from repeated updating.

Keywords:

Adaptivity, Bayesian Statistics, central limit theorem. importance
sampling, Kullback divergence, law of large numbers, MCMC algorithm,
population Monte Carlo, proposal distribution, Rao-Blackwellisation.