Adaptive Importance Sampling for Reliability Analysis

Resumo

Several numerical schemes have been proposed in the last decades to address the problem of reliability
analysis (i.e. evaluation of the probability of failure). Among these, a very popular method is Importance Sampling
(IS), where the probability distribution employed for sampling is different from that of the random variables. It is
known that by appropriate choice of the sampling distribution it is possible to reduce the variance of the estimate
and thus obtain more accurate results. However, it is often difficult to known beforehand what is an appropriate
sampling distribution for IS in practice. In order to avoid this difficulty, in the last years researchers developed
Adaptive Importance Sampling (AIS) techniques. The idea of AIS is to take an initial sampling distribution, draw
a sample, evaluate the required statistical moments and then improve the sampling distribution using some update
rule. In this work we compare some of the existing AIS techniques in the context of Reliability Analysis.