Tuning of adaptive interacting particle system for rare event probability estimation

Abstract

The interacting particle system (IPS) for rare event algorithm has been well mathematically formulated, with a wide variety of results on the estimation accuracy of the probability of rare event. Despite this theoretical point of view, the practical side of this algorithm has not been handled completely. Indeed, a tuning parameter has a significant influence on the effective algorithm performance. Moreover, the choice of a good parameter value often proves to be fastidious and may decrease the usefulness of the IPS algorithm. Therefore, we propose a statistical technique in order to make the IPS algorithm fully adaptive. We derive this strategy for threshold exceedance probability estimation and for the estimation of probability density function tail. The performances of the proposed method have been studied on a toy case and on two more complex estimation problems in optical fiber and financial engineering.