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A note on the choice and the estimation of Kriging models for the analysis of deterministic computer experiments
Author(s) -
Ginsbourger David,
Dupuy Delphine,
Badea Anca,
Carraro Laurent,
Roustant Olivier
Publication year - 2009
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.741
Subject(s) - kriging , computer science , dimension (graph theory) , field (mathematics) , maximization , estimation , mathematical optimization , econometrics , mathematics , machine learning , management , pure mathematics , economics
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.