Rare Event Simulation

TL;DR

This paper reviews advanced stochastic simulation methods like Monte Carlo, Importance Sampling, and Subset Simulation for efficiently estimating rare-event probabilities in highly reliable dynamic systems.

Contribution

It provides an overview of methods specifically designed to improve the efficiency of rare-event probability estimation in complex systems.

Findings

Importance Sampling reduces variance in estimates.

Subset Simulation efficiently handles very low probabilities.

Monte Carlo remains a baseline method with limitations.

Abstract

Rare events are events that are expected to occur infrequently, or more technically, those that have low probabilities (say, order of $10^{-3}$ or less) of occurring according to a probability model. In the context of uncertainty quantification, the rare events often correspond to failure of systems designed for high reliability, meaning that the system performance fails to meet some design or operation specifications. As reviewed in this section, computation of such rare-event probabilities is challenging. Analytical solutions are usually not available for non-trivial problems and standard Monte Carlo simulation is computationally inefficient. Therefore, much research effort has focused on developing advanced stochastic simulation methods that are more efficient. In this section, we address the problem of estimating rare-event probabilities by Monte Carlo simulation, Importance Sampling and Subset Simulation for highly reliable dynamic systems.