Adaptive Importance Sampling in General Mixture Classes

In this paper, we propose an adaptive algorithm that iteratively updates both the weights and component parameters of a mixture importance sampling density so as to optimise the performance of importance sampling, as measured by an entropy criterion. The method, called M-PMC, is shown to be applicable to a wide class of importance sampling densities, which includes in particular mixtures of multivariate Student $t$ distributions. The performance of the proposed scheme is studied on both artificial and real examples, highlighting in particular the benefit of a novel Rao-Blackwellisation device which can be easily incorporated in the updating scheme