Estimation of the volume of an excursion set of a Gaussian process using intrinsic Kriging

2006/11/09 by Emmanuel Vazquez, Vazquez, Emmanuel, Miguel Piera Martinez +1 · 1 citation
Mathematics · #60G15 #60G25 #60G70 #62K99 #62M20 #FOS: Mathematics #Statistics Theory (math.ST) #math.ST #msc:60G15 #msc:60G25 #msc:60G70 #msc:62K99 #msc:62M20 #stat.TH

paper · pdf · doi:10.48550/arxiv.math/0611273

11 pages, 1 figure

arxiv created 2006/11/09 · arxiv updated 2009/12/01

Abstract

Assume that a Gaussian process ξ is predicted from n pointwise observations by intrinsic Kriging and that the volume of the excursion set of ξ above a given threshold u is approximated by the volume of the predictor. The first part of this paper gives a bound on the convergence rate of the approximated volume. The second part describes an algorithm that constructs a sequence of points to yield a fast convergence of the approximation. The estimation of the volume of an excursion set is a highly relevant problem for the industrial world since it corresponds to the estimation of the failure probability of a system that is known only through sampled observations.

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