Open Access
June 2012 Efficient Monte Carlo for high excursions of Gaussian random fields
Robert J. Adler, Jose H. Blanchet, Jingchen Liu
Ann. Appl. Probab. 22(3): 1167-1214 (June 2012). DOI: 10.1214/11-AAP792


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.


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Robert J. Adler. Jose H. Blanchet. Jingchen Liu. "Efficient Monte Carlo for high excursions of Gaussian random fields." Ann. Appl. Probab. 22 (3) 1167 - 1214, June 2012.


Published: June 2012
First available in Project Euclid: 18 May 2012

zbMATH: 1251.60031
MathSciNet: MR2977989
Digital Object Identifier: 10.1214/11-AAP792

Primary: 60G15 , 65C05
Secondary: 60G60 , 62G32

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

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.22 • No. 3 • June 2012
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