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Assessment of uncertainty in computer experiments from Universal to Bayesian Kriging

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  • C. Helbert
  • D. Dupuy
  • L. Carraro

Abstract

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.

Suggested Citation

  • C. Helbert & D. Dupuy & L. Carraro, 2009. "Assessment of uncertainty in computer experiments from Universal to Bayesian Kriging," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(2), pages 99-113, March.
  • Handle: RePEc:wly:apsmbi:v:25:y:2009:i:2:p:99-113
    DOI: 10.1002/asmb.743
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    References listed on IDEAS

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    1. Jeremy E. Oakley & Anthony O'Hagan, 2004. "Probabilistic sensitivity analysis of complex models: a Bayesian approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(3), pages 751-769, August.
    2. Dale Zimmerman & Noel Cressie, 1992. "Mean squared prediction error in the spatial linear model with estimated covariance parameters," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 44(1), pages 27-43, March.
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    Cited by:

    1. Risk, J. & Ludkovski, M., 2016. "Statistical emulators for pricing and hedging longevity risk products," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 45-60.
    2. 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.
    3. James Risk & Michael Ludkovski, 2015. "Statistical Emulators for Pricing and Hedging Longevity Risk Products," Papers 1508.00310, arXiv.org, revised Sep 2015.
    4. Roustant, Olivier & Ginsbourger, David & Deville, Yves, 2012. "DiceKriging, DiceOptim: Two R Packages for the Analysis of Computer Experiments by Kriging-Based Metamodeling and Optimization," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 51(i01).

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