A double proposal normalized importance sampling estimator

International audienceMonte Carlo methods rely on random sampling to compute and approximate expectations of interest in signal processing. Among Monte Carlo methods for integration, Importance Sampling is a variance reduction technique which consists in sampling from an importance distribution which is not necessary the original target distribution. The performance of the resulting estimate is strongly related to the critical choice of such an important distribution. In this paper we revisit the rationale of the normalized importance sampling technique and show that it is possible to improve the classical importance sampling estimate by approximating the expectation of interest via two importance distributions. The choice of these two importance distributions is optimized w.r.t. the variance of the final estimate. Our results are validated via numerical simulation