The Annals of Applied Probability

Efficient Monte Carlo for high excursions of Gaussian random fields

Robert J. Adler, Jose H. Blanchet, and Jingchen Liu

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Our focus is on the design and analysis of efficient Monte Carlo methods for computing tail probabilities for the suprema of Gaussian random fields, along with conditional expectations of functionals of the fields given the existence of excursions above high levels, b. Naïve Monte Carlo takes an exponential, in b, computational cost to estimate these probabilities and conditional expectations for a prescribed relative accuracy. In contrast, our Monte Carlo procedures achieve, at worst, polynomial complexity in b, assuming only that the mean and covariance functions are Hölder continuous. We also explain how to fine tune the construction of our procedures in the presence of additional regularity, such as homogeneity and smoothness, in order to further improve the efficiency.

Article information

Ann. Appl. Probab., Volume 22, Number 3 (2012), 1167-1214.

First available in Project Euclid: 18 May 2012

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Zentralblatt MATH identifier

Primary: 60G15: Gaussian processes 65C05: Monte Carlo methods
Secondary: 60G60: Random fields 62G32: Statistics of extreme values; tail inference

Gaussian random fields high-level excursions Monte Carlo tail distributions efficiency


Adler, Robert J.; Blanchet, Jose H.; Liu, Jingchen. Efficient Monte Carlo for high excursions of Gaussian random fields. Ann. Appl. Probab. 22 (2012), no. 3, 1167--1214. doi:10.1214/11-AAP792.

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