Estimation of the volume of an excursion set of a Gaussian process using intrinsic Kriging
arXiv:math/0611273
Abstract
Assume that a Gaussian process is predicted from pointwise observations by intrinsic Kriging and that the volume of the excursion set of above a given threshold 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.
11 pages, 1 figure