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

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  • David Ginsbourger
  • Delphine Dupuy
  • Anca Badea
  • Laurent Carraro
  • Olivier Roustant

Abstract

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.

Suggested Citation

  • David Ginsbourger & Delphine Dupuy & Anca Badea & Laurent Carraro & Olivier Roustant, 2009. "A note on the choice and the estimation of Kriging models for the analysis of deterministic computer experiments," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(2), pages 115-131, March.
    • Handle: RePEc:wly:apsmbi:v:25:y:2009:i:2:p:115-131
    DOI: 10.1002/asmb.741
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    References listed on IDEAS

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    1. Markus Abt, 1999. "Estimating the Prediction Mean Squared Error in Gaussian Stochastic Processes with Exponential Correlation Structure," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(4), pages 563-578, December.
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    Cited by:

    1. Xiao, Qian & Xu, Hongquan, 2021. "A mapping-based universal Kriging model for order-of-addition experiments in drug combination studies," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    2. Jize Zhang & Alexandros A. Taflanidis & Norberto C. Nadal-Caraballo & Jeffrey A. Melby & Fatimata Diop, 2018. "Advances in surrogate modeling for storm surge prediction: storm selection and addressing characteristics related to climate change," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 94(3), pages 1225-1253, December.
    3. Loïc Iapteff & Julien Jacques & Matthieu Rolland & Benoit Celse, 2021. "Reducing the number of experiments required for modelling the hydrocracking process with kriging through Bayesian transfer learning," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(5), pages 1344-1364, November.

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