title: Efficient prediction designs for random fields.
abstract: For estimation and predictions of random fields, it is increasingly acknowledged that the kriging variance may be a poor representative of true uncertainty. Experimental designs based on more elaborate criteria that are appropriate for empirical kriging (EK) are then often non-space-filling and very costly to determine. In this paper, we investigate the possibility of using a compound criterion inspired by an equivalence theorem type relation to build designs quasi-optimal for the EK variance when space-filling designs become unsuitable. Two algorithms are proposed, one relying on stochastic optimization to explicitly identify the Pareto front, whereas the second uses the surrogate criteria as local heuristic to choose the points at which the (costly) true EK variance is effectively computed. We illustrate the performance of the algorithms presented on both a simple simulated example and a real oceanographic dataset. © 2014 The Authors.Applied Stochastic Models in Business and Industrypublished by John Wiley & Sons, Ltd.
authors: Department of Applied Statistics, Johannes-Kepler-University of Linz Linz, Austria.
authors: Werner G
authors: WG
authors: Müller
authors: Laboratoire I3S, CNRS/Université de Nice-Sophia Antipolis Nice, France.
authors: Luc
authors: L
authors: Pronzato
authors: Laboratoire I3S, CNRS/Université de Nice-Sophia Antipolis Nice, France.
authors: Joao
authors: J
authors: Rendas
authors: Department of Applied Statistics, Johannes-Kepler-University of Linz Linz, Austria.
authors: Helmut
authors: H
authors: Waldl
keywords: Gaussian process models; Pareto front; empirical kriging; optimal design