Importance sampling with transformed weights

摘要

The importance sampling (IS) method lies at the core of many MonteCarlo-based techniques. IS allows the approximation of a target probabilitydistribution by drawing samples from a proposal (or importance) distribution,different from the target, and computing importance weights (IWs) that accountfor the discrepancy between these two distributions. The main drawback of ISschemes is the degeneracy of the IWs, which significantly reduces theefficiency of the method. It has been recently proposed to use transformed IWs(TIWs) to alleviate the degeneracy problem in the context of Population MonteCarlo, which is an iterative version of IS. However, the effectiveness of thistechnique for standard IS is yet to be investigated. In this letter wenumerically assess the performance of IS when using TIWs, and show that themethod can attain robustness to weight degeneracy thanks to a bias/variancetrade-off.