Uniformly Efficient Simulation for Extremes of Gaussian Random Fields

TL;DR

This paper introduces a new simulation method that efficiently estimates rare-event probabilities across a broad class of Gaussian random fields, reducing computational costs for multiple events.

Contribution

It proposes a uniformly efficient estimator applicable to a wide range of Gaussian fields, improving over traditional methods that are event-specific.

Findings

The estimator is asymptotically efficient.

The estimator demonstrates uniform efficiency.

Simulation studies confirm effectiveness.

Abstract

This paper considers the problem of simultaneously estimating rare-event probabilities for a class of Gaussian random fields. A conventional rare-event simulation method is usually tailored to a specific rare event and consequently would lose estimation efficiency for different events of interest, which often results in additional computational cost in such simultaneous estimation problem. To overcome this issue, we propose a uniformly efficient estimator for a general family of H\"older continuous Gaussian random fields. We establish the asymptotic and uniform efficiency of the proposed method and also conduct simulation studies to illustrate its effectiveness.