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We explore past and recent developments in rare-event probability estimationwith a particular focus on a novel Monte Carlo technique Empirical LikelihoodMaximization (ELM). This is a versatile method that involves sampling from asequence of densities using MCMC and maximizing an empirical likelihood. Thequantity of interest, the probability of a given rare-event, is estimated bysolving a convex optimization program related to likelihood maximization.Numerical experiments are performed using this new technique and benchmarks aregiven against existing robust algorithms and estimators.

Rare-event Probability Estimation via Empirical Likelihood Maximization