Estimation of rare event probabilities using cross-entropy

This paper deals with estimation of probabilities of rare events in static simulation models using a fast adaptive two-stage procedure based on importance sampling and Kullback-Liebler's cross-entropy (CE). More specifically, at the first stage we estimate the optimal parameter vector in the importance sampling distribution using CE, and at the second stage we estimate the desired rare event probability using importance sampling (likelihood ratios). Some theoretical aspects of the proposed method, including its convergence, are established. The numerical results presented suggest that the method effectively estimates rare event probabilities.