Subset Adaptive Importance Sampling for Multi-Failure-Region Estimation

Abstract

Rare-event estimation is a relevant problem in statistical signal processing. While significant efforts have been devoted to unimodal problems, the case of multimodal scenarios is still hard to tackle with state-of-the-art methods. In this paper, we propose the subset adaptive importance sampling (SAIS) algorithm for the estimation of rare events in the context of Bayesian signal processing. The new algorithm incorporates advantages from subset simulation techniques and from adaptive importance sampling, in particular population Monte Carlo methods. It provides a multilevel estimation of the failure probability and balances the trade-off between exploration and exploitation of the failure space in the adaptation. The algorithm is particularly well suited for multimodal scenarios. We further introduce adaptation rules for more efficient sampling. Finally, we test the good performance of the proposed algorithm in numerical examples.