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Classic Kriging versus Kriging with bootstrapping or conditional simulation: classic Kriging’s robust confidence intervals and optimization

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  • Ehsan Mehdad

    (Tilburg University, Tilburg, the Netherlands)

  • Jack P C Kleijnen

    (Tilburg University, Tilburg, the Netherlands)

Abstract

Kriging is a popular method for estimating the global optimum of a simulated system. Kriging approximates the input/output function of the simulation model. Kriging also estimates the variances of the predictions of outputs for input combinations not yet simulated. These predictions and their variances are used by ‘efficient global optimization’ (EGO), to balance local and global search. This article focuses on two related questions: (1) How to select the next combination to be simulated when searching for the global optimum? (2) How to derive confidence intervals for outputs of input combinations not yet simulated? Classic Kriging simply plugs the estimated Kriging parameters into the formula for the predictor variance, so theoretically this variance is biased. This article concludes that practitioners may ignore this bias, because classic Kriging gives acceptable confidence intervals and estimates of the optimal input combination. This conclusion is based on bootstrapping and conditional simulation.

Suggested Citation

  • Ehsan Mehdad & Jack P C Kleijnen, 2015. "Classic Kriging versus Kriging with bootstrapping or conditional simulation: classic Kriging’s robust confidence intervals and optimization," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(11), pages 1804-1814, November.
    • Handle: RePEc:pal:jorsoc:v:66:y:2015:i:11:p:1804-1814
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    Citations

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    Cited by:

    1. Kleijnen, J.P.C. & Mehdad, Ehsan, 2015. "Estimating the Variance of the Predictor in Stochastic Kriging," Discussion Paper 2015-041, Tilburg University, Center for Economic Research.
    2. Xi Chen & Kyoung-Kuk Kim, 2016. "Efficient VaR and CVaR Measurement via Stochastic Kriging," INFORMS Journal on Computing, INFORMS, vol. 28(4), pages 629-644, November.
    3. Chen, Xi & Zhou, Qiang, 2017. "Sequential design strategies for mean response surface metamodeling via stochastic kriging with adaptive exploration and exploitation," European Journal of Operational Research, Elsevier, vol. 262(2), pages 575-585.

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