We explore past and recent developments in rare-event probability estimation with a particular focus on a novel Monte Carlo technique Empirical Likelihood Maximization (ELM). This is a versatile method that involves sampling from a sequence of densit
ies using MCMC and maximizing an empirical likelihood. The quantity of interest, the probability of a given rare-event, is estimated by solving a convex optimization program related to likelihood maximization. Numerical experiments are performed using this new technique and benchmarks are given against existing robust algorithms and estimators.
