### Abstract

The Cross-Entropy method is a new Monte Carlo paradigm pioneered by Rubinstein (1999) in Operation Research. Its primary applications are (i) the calculation of probability of rare events, and (ii) the optimisation of irregular, multi-modal functions. While these two objectives seem to have a little in common, the CE approach manages to express them in a similar framework. In this talk, we will explain how Statistics can benefit from the CE method, and how the CE method can also benefit in turn from Statistical methodology. We will discuss the following particular applications in Statistics: Monte-Carlo p-values, simulation of truncated distributions, variable selection, and mixture estimation. We will see that in each case CE provides significant improvements over current methods. Interestingly, we will see also vanilla CE rarely works directly, but tandard tools from Statistical Inference allow for developing more efficient algorithms. In particular, we will discuss a CE-EM algorithm for mixture estimation, which outperform any straight CE or EM algorithm, in terms, of finding higher modes of the likelihood function.