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As already explained in previous chapters, rare event simulation requires acceleration techniques to speed up the occurrence of the rare events under consideration, otherwise it may take unacceptably large sample sizes to get enough positive realizations, or even a single one, on average. On the other hand, accelerating too much can be counterproductive and even lead to a variance explosion and/or an increase in the computation time. Therefore, an appropriate balance must be achieved, and this is not always easy. This difficulty was highlighted in the previous chapter when discussing the importance sampling (IS) technique, the idea of which is to change the probability laws driving the model in order to make the events of interest more likely, and to correct the bias by multiplying the estimator by the appropriate likelihood ratio.

In this chapter, we review an alternative technique called splitting, which accelerates …