IMPERIAL COLLEGE LONDON, HUXLEY BUILDING
Please note that the cancelled seminar scheduled for the 28th of October has been replaced by:
Minimum variance importance sampling via Population Monte Carlo
Professor Christian P. Robert (CEREMADE, Universite Paris Dauphine & CREST-INSEE)
Friday 28 October 2005 3-4 pm
139
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 raises 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. In particular, since variance reduction has always been a central issue in Monte Carlo experiments, we show that population Monte Carlo can be used to this effect, in that a mixture of importance functions, called a D-kernel, can be iteratively optimised to achieve the minimum asymptotic variance for a function of interest among all possible mixtures.The implementation of this iterative scheme is illustrated for the computation of the price of a Europeanoption in the Cox-Ingersoll-Ross model.
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