In (Cappé et al., 2004) we proposed a simulation scheme termed Population Monte Carlo which may be viewed as an Iterated Importance Sampling approach, with resampling and Markovian instrumental simulations. This scheme also is a particular case of the Sequential Monte Carlo Sampling approach of (Delmoral et al., 2006). I will discuss the Population Monte Carlo approach, focussing on the case where the target distribution is held fixed and the importance kernels are adapted during the iterations in order to optimize a performance criterion. In the case where the importance kernel is composed of a mixture of fixed kernels, the mixture weights can be adapted using update rules which are remarkably stable and have interesting connections with the Expectation-Maximization algorithm.
This talk is based on work done with (or by) several of my colleague in Paris - Arnaud Guillin, Jean-Michel Marin, Christian P. Robert (Cérémade) and Randal Douc (École Polytechnique) - as well as on ideas related to the ECOSSTAT project.