Multiple importance sampling with overlapping sets of proposals

In this paper, we introduce multiple importance sampling (MIS) approaches with overlapping (i.e., non-disjoint) sets of proposals. We derive a novel weighting scheme, based on the deterministic mixture methodology, that leads to unbiased estimators. The proposed framework can be seen as a generalization of other well-known MIS algorithms available in the literature. Furthermore, it allows us to achieve any desired trade-off between the variance of the estimators and the computational complexity through the definition of the sets of proposals. Simulations using a bimodal target density show the good performance of the proposed approach.