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Monotonicity-Preserving Bootstrapped Kriging Metamodels for Expensive Simulations

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  • Kleijnen, Jack P.C.

    (Tilburg University, School of Economics and Management)

  • van Beers, W.C.M.

    (Tilburg University, School of Economics and Management)

Abstract

Kriging metamodels (also called Gaussian process or spatial correlation models) approximate the Input/Output functions implied by the underlying simulation models. Such metamodels serve sensitivity analysis, especially for computationally expensive simulations. In practice, simulation analysts often know that this Input/Output function is monotonic. To obtain a Kriging metamodel that preserves this characteristic, this article uses distribution-free bootstrapping assuming each input combination is simulated several times to obtain more reliable averaged outputs. Nevertheless, these averages still show sampling variation, so the Kriging metamodel does not need to be an exact interpolator; bootstrapping gives a noninterpolating Kriging metamodel. Bootstrapping may use standard Kriging software. The method is illustrated through the popular M/M/1 model with either the mean or the 90% quantile as output; these outputs are monotonic functions of the traffic rate. The empirical results demonstrate that monotonicity-preserving bootstrapped Kriging gives higher probability of covering the true outputs, without lengthening the confidence interval.
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Suggested Citation

  • Kleijnen, Jack P.C. & van Beers, W.C.M., 2009. "Monotonicity-Preserving Bootstrapped Kriging Metamodels for Expensive Simulations," Other publications TiSEM 59d5c29b-25a3-4af9-921f-b, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiutis:59d5c29b-25a3-4af9-921f-bf3a28d93a38
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    References listed on IDEAS

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    1. D den Hertog & J P C Kleijnen & A Y D Siem, 2006. "The correct Kriging variance estimated by bootstrapping," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(4), pages 400-409, April.
    2. Kleijnen, Jack P.C., 2009. "Kriging metamodeling in simulation: A review," European Journal of Operational Research, Elsevier, vol. 192(3), pages 707-716, February.
    3. Xing Jin & Michael C. Fu & Xiaoping Xiong, 2003. "Probabilistic Error Bounds for Simulation Quantile Estimators," Management Science, INFORMS, vol. 49(2), pages 230-246, February.
    4. Guangwu Liu & Liu Jeff Hong, 2009. "Kernel estimation of quantile sensitivities," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(6), pages 511-525, September.
    5. Bruce Ankenman & Barry L. Nelson & Jeremy Staum, 2010. "Stochastic Kriging for Simulation Metamodeling," Operations Research, INFORMS, vol. 58(2), pages 371-382, April.
    6. Jack P. C. Kleijnen, 2009. "Factor Screening in Simulation Experiments: Review of Sequential Bifurcation," International Series in Operations Research & Management Science, in: Christos Alexopoulos & David Goldsman & James R. Wilson (ed.), Advancing the Frontiers of Simulation, pages 153-167, Springer.
    7. Jack P.C. Kleijnen, 2015. "Design and Analysis of Simulation Experiments," International Series in Operations Research and Management Science, Springer, edition 2, number 978-3-319-18087-8, April.
    8. L. Jeff Hong, 2009. "Estimating Quantile Sensitivities," Operations Research, INFORMS, vol. 57(1), pages 118-130, February.
    9. Batur, D. & Choobineh, F., 2010. "A quantile-based approach to system selection," European Journal of Operational Research, Elsevier, vol. 202(3), pages 764-772, May.
    10. Michael C. Fu & L. Jeff Hong & Jian-Qiang Hu, 2009. "Conditional Monte Carlo Estimation of Quantile Sensitivities," Management Science, INFORMS, vol. 55(12), pages 2019-2027, December.
    11. Peter Frazier & Warren Powell & Savas Dayanik, 2009. "The Knowledge-Gradient Policy for Correlated Normal Beliefs," INFORMS Journal on Computing, INFORMS, vol. 21(4), pages 599-613, November.
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    Cited by:

    1. Cousin, Areski & Maatouk, Hassan & Rullière, Didier, 2016. "Kriging of financial term-structures," European Journal of Operational Research, Elsevier, vol. 255(2), pages 631-648.
    2. Kleijnen, Jack P.C., 2017. "Regression and Kriging metamodels with their experimental designs in simulation: A review," European Journal of Operational Research, Elsevier, vol. 256(1), pages 1-16.

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    More about this item

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C9 - Mathematical and Quantitative Methods - - Design of Experiments

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