Uniformly efficient simulation for extremes of Gaussian random fields

Abstract

This paper considers the problem of simultaneously estimating rare-event probabilities for a class of Gaussian random fields. A conventional rareevent 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 Hölder continuous Gaussian random fields.We establish the asymptotic and uniform efficiency of the proposed method and also conduct simulation studies to illustrate its effectiveness.

How sharp are classical approximations for statistical applications?

“…Other method. For completeness we must cite the work of Li and Xu (2018) which is dedicated to a method of importance sampling for rare events simulations applied to high values of random fields. Their method is very accurate for very high levels, typically P{M T > u} 10 −6 or 10 −12 .…”

Speeding up Monte Carlo simulations for the adaptive sum of powered score test with importance sampling

“…The proposed distribution is often called a proposal distribution. This method has been frequently used to evaluate the extremes of Gaussian random fields and other rare‐event probabilities, and its efficiency has been carefully studied (Adler et al ., 2012; Liu and Xu, 2014a, 2014b; Jiang et al ., 2017; He and Xu, 2018; Li and Xu, 2018). Since the p ‐value calculation involves sampling from a rejection region with possibly a small probability from a null distribution, we propose using importance sampling to speed up the SPU and aSPU tests.…”