Efficient simulation for dependent rare events with applications to extremes

TL;DR

This paper introduces new estimators and variance reduction techniques for efficiently estimating probabilities of dependent rare events, especially in extreme cases, with demonstrated numerical performance.

Contribution

It proposes a flexible series of estimators and variance reduction schemes for dependent rare event probabilities, with theoretical efficiency analysis.

Findings

Estimators show improved efficiency in rare-event simulations.

Variance reduction schemes significantly decrease estimator variance.

Numerical examples validate the effectiveness of the proposed methods.

Abstract

We consider the general problem of estimating probabilities which arise as a union of dependent events. We propose a flexible series of estimators for such probabilities, and describe variance reduction schemes applied to the proposed estimators. We derive efficiency results of the estimators in rare-event settings, in particular those associated with extremes. Finally, we examine the performance of our estimators in a numerical example.