A Comparison Of Clipping Strategies For Importance Sampling

Importance Sampling (IS) methods approximate a targeted distribution with a set of weighted samples, drawn from a proposal distribution. Unfortunately, a mismatch between the proposal and the targeted distribution may endanger the performance of the estimators. In this paper, we focus on the so-called nonlinear IS (NIS) framework, where a nonlinear function is applied to the standard importance weights (IWs). The aim of this transformation is to mitigate the well-known problem of the degeneracy of the IWs by controlling the weight variability. We consider the clipping transformation and test its robustness with respect to the choice of the clipping value. We also propose a novel NIS methodology, where not only a subset of weights is modified a posteriori, but also the corresponding samples are moved. We compare these NIS schemes with standard IS and Monte Carlo methods by means of illustrative numerical examples.