A note on the choice and the estimation of Kriging models for the analysis of deterministic computer experiments

• Published in: Applied stochastic models in business and industry Vol. 25; no. 2; pp. 115 - 131
• Main Authors: Ginsbourger, David, Dupuy, Delphine, Badea, Anca, Carraro, Laurent, Roustant, Olivier
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01.03.2009
• Subjects: additive models; deterministic drift; Kriging; maximum likelihood; metamodeling
• ISSN: 1524-1904; 1526-4025
• DOI: 10.1002/asmb.741

Our goal in the present article to give an insight on some important questions to be asked when choosing a Kriging model for the analysis of numerical experiments. We are especially concerned about the cases where the size of the design of experiments is relatively small to the algebraic dimension of the inputs. We first fix the notations and recall some basic properties of Kriging. Then we expose two experimental studies on subjects that are often skipped in the field of computer simulation analysis: the lack of reliability of likelihood maximization with few data and the consequences of a trend misspecification. We finally propose an example from a porous media application, with the introduction of an original Kriging method in which a non‐linear additive model is used as an external trend. Copyright © 2009 John Wiley & Sons, Ltd.