Rare-event Probability Estimation via Empirical Likelihood Maximization

TL;DR

This paper introduces Empirical Likelihood Maximization (ELM), a new Monte Carlo method for estimating rare-event probabilities by combining MCMC sampling with empirical likelihood optimization, validated through numerical experiments.

Contribution

The paper presents ELM, a novel Monte Carlo approach that integrates MCMC sampling with empirical likelihood maximization for efficient rare-event probability estimation.

Findings

ELM outperforms existing algorithms in numerical experiments.

ELM provides a versatile framework applicable to various rare-event problems.

Benchmark comparisons show improved accuracy and efficiency of ELM.

Abstract

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.