Robust mixture populationmonte Carlo scheme with adaptation of the number of components

We address the Monte Carlo approximation of probability distributions in high-dimensional spaces. In particular, we investigate the population Monte Carlo (PMC) scheme, which is based on an iterative importance sampling approach, and its extension the mixture-PMC method (MPMC), which models the importance functions as mixtures of kernels. We propose an extension of the MPMC method which incorporates adaptation of the number of mixture components, and applies a nonlinear transformation to the importance weights in order to smooth their variations and avoid degeneracy problems. We present numerical results that illustrate the performance improvement attained by the new method.