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Efficient prediction designs for random fields
Author(s) -
Müller Werner G.,
Pronzato Luc,
Rendas Joao,
Waldl Helmut
Publication year - 2014
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.2084
Subject(s) - kriging , mathematical optimization , equivalence (formal languages) , variance (accounting) , heuristic , computer science , simple (philosophy) , range (aeronautics) , relation (database) , design of experiments , mathematics , algorithm , statistics , data mining , machine learning , engineering , philosophy , accounting , epistemology , discrete mathematics , business , aerospace engineering
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 Industry published by John Wiley & Sons, Ltd.