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Assessment of uncertainty in computer experiments from Universal to Bayesian Kriging
Author(s) -
Helbert C.,
Dupuy D.,
Carraro L.
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.743
Subject(s) - kriging , bayesian probability , geostatistics , variance (accounting) , computer science , variogram , econometrics , interpretation (philosophy) , statistics , data mining , algorithm , mathematics , machine learning , artificial intelligence , spatial variability , business , programming language , accounting
Kriging was first introduced in the field of geostatistics. Nowadays, it is widely used to model computer experiments. Since the results of deterministic computer experiments have no experimental variability, Kriging is appropriate in that it interpolates observations at data points. Moreover, Kriging quantifies prediction uncertainty, which plays a major role in many applications. Among practitioners we can distinguish those who use Universal Kriging where the parameters of the model are estimated and those who use Bayesian Kriging where model parameters are random variables. The aim of this article is to show that the prediction uncertainty has a correct interpretation only in the case of Bayesian Kriging. Different cases of prior distributions have been studied and it is shown that in one specific case, Bayesian Kriging supplies an interpretation as a conditional variance for the prediction variance provided by Universal Kriging. Finally, a simple petroleum engineering case study presents the importance of prior information in the Bayesian approach. Copyright © 2009 John Wiley & Sons, Ltd.