A preliminary study of optimal splitting for rare-event simulation

Efficiency is a big concern when using simulation to estimate rare-event probabilities, since a huge number of simulation replications may be needed in order to obtain a reasonable estimate of such a probability. Furthermore, when multiple designs must be compared, and each design requires simulation of a rare event, then the total number of samples across all designs can be prohibitively high. This paper presents a new approach to enhance the efficiency for rare-event simulation. Our approach is developed by integrating the notions of level splitting and optimal computing budget allocation. The goal is to determine the optimal numbers of simulation runs across designs and across a number of splitting levels so that the variance of the rare-event estimator is minimized.