  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 densities 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.
