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