Dr. Víctor Elvira (University of Edinburgh) – Multiple and adaptive importance sampling

Importance sampling (IS) is an elegant, theoretically sound, flexible, and simple-to-understand methodology for approximation of intractable integrals and probability distributions. The only requirement is the point-wise evaluation of the targeted distribution. The basic mechanism of IS consists of (a) drawing samples from simple proposal densities, (b) weighting the samples by accounting for the mismatch between the targeted and the proposal densities, and (c) approximating the moments of interest with the weighted samples. The performance of IS methods directly depends on the choice of the proposal functions. For that reason, the proposals have to be updated and improved with iterations so that samples are generated in regions of interest. In this talk, we will first introduce the basics of IS and multiple IS (MIS), motivating the need to use several proposal densities. Then, the focus will be on motivating the use of adaptive IS (AIS) algorithms, describing an encompassing framework of recent methods in the current literature. Finally, we review the problem of combining Monte Carlo estimators in the context of MIS and AIS.