Efficient Multiple Importance Sampling Estimators

TL;DR

This paper introduces a new multiple importance sampling estimator that balances variance reduction and computational efficiency by partitioning proposal distributions, demonstrating superior performance through simulations.

Contribution

A novel partial deterministic mixture MIS estimator that offers an efficient compromise between variance reduction and computational complexity.

Findings

Shows improved variance reduction over classical methods

Achieves computational efficiency comparable to simpler approaches

Demonstrates superior performance in simulation experiments

Abstract

Multiple importance sampling (MIS) methods use a set of proposal distributions from which samples are drawn. Each sample is then assigned an importance weight that can be obtained according to different strategies. This work is motivated by the trade-off between variance reduction and computational complexity of the different approaches (classical vs. deterministic mixture) available for the weight calculation. A new method that achieves an efficient compromise between both factors is introduced in this paper. It is based on forming a partition of the set of proposal distributions and computing the weights accordingly. Computer simulations show the excellent performance of the associated \mbox{\emph{partial deterministic mixture} MIS estimator.