An extended maximum entropy method for estimation of rare event probabilities

Abstract

The maximum entropy model that maximizes the entropy function under a set of constraints derived from the simulation samples has been used for estimating probability distributions. We propose the use of the maximum entropy model for estimating rare event probabilities from the simulation samples. To improve estimation of the far tail part, the entropy maximization problem is generalized by relaxing the head part constraints and focusing on the tail part sample information. The generalized maximum entropy model is formulated as a convex optimization problem in a normed linear vector space. Global optimality of the Lagrangian solution and the asymptotic consistency of the solution sequence for the increased sample sizes are proved. We discuss implementation issues such as parameter estimation methods, solution procedures, and model selection techniques based on accelerated simulation.