Underestimation of Rare Event Probabilities in Importance Sampling Simulations

The researcher faced with a computationally intensive simulation will either seek powerful processing capabilities or turn to variance reduction techniques. In many situations, a combination of both approaches is required to achieve the desired accuracy. In the study of rare events, importance sampling (IS) is the only variance reduction technique which has been shown to offer the potential for substantial run time improvement. Indeed the dramatic improvements in run time demonstrated in the literature is strong motivation for the researcher to adopt IS as a day-today simulation tool. For this reason, it is important to have a clear understanding of the problems inherent in IS as well as the possibilities for improvement it offers. Hence in this paper, we discuss the potential problem with IS in underestimating the probability of rare events. We describe and illustrate the problem and suggest diagnostic plots to check for its occurrence. These diagnostics are quick and simple to use in any simulation and give the experimenter an easily interpreted output to identify the possible presence of underestimation in the simulation.