Rare-event Probability Estimation via Empirical Likelihood Maximization

2013/12/11 by Alan Huang, A. Huang, Huang, A. +3
Decision Sciences · Mathematics · #Computation (stat.CO) #FOS: Computer and information sciences #Markov Chains and Monte Carlo Methods #Probability and Risk Models #Statistical Methods and Inference #stat.CO

paper · pdf · doi:10.48550/arxiv.1312.3027

arxiv created 2013/12/11 · openalex publication_date 2013/12/11 · arxiv updated 2013/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Large Sample Properties of Generalized Method of Moments Estimators
• Monte Carlo sampling methods using Markov chains and their applications

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