## Section: New Results

### Soft level splitting for rare event estimation

Participants : Frédéric Cérou, Arnaud Guyader.

This is a collaboration with Nicolas Hengartner (Los Alamos).

It is well established now that one can use adaptive splitting levels to compute the conditional probabilities of nested sets. To get an efficient algorithm, the probability of a set given the previous one should be always the same, which is approximately achieved adaptively by using the empirical cdf (cumulative distribution function) of the scores. The way to proceed is to fix a probability of success ${p}_{0}$, and then choose the ${p}_{0}$ quantile of the current scores. Here we investigate whether, by using the whole cdf, and not only one quantile, we can design an algorithm with better performance. The main trick is a transformation to have a sample of exponential variables. This would require the knowledge of the cdf of the cost, which is obviously unvailable, but we can replace it by the empirical cdf of the sample at the previous level. The complete theoretical study of this algorithm is still to be done, but we have illustrated by some examples that it can lead to significantly better results than the standard splitting procedure with the same number of intermediate levels.