Monotonicity-preserving bootstrapped kriging metamodels for expensive simulations

Jack P.C. Kleijnen, W.C.M. van Beers

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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.
Original languageEnglish
Pages (from-to)708-717
JournalThe Journal of the Operational Research Society
Volume64
Issue number5
Publication statusPublished - 2013

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Sensitivity analysis
Sampling
Metamodel
Simulation
Kriging
Monotonicity
Bootstrapping
Empirical results
Analysts
Confidence interval
Gaussian process
Software
Distribution-free
Simulation model
Spatial correlation
Quantile

Cite this

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title = "Monotonicity-preserving bootstrapped kriging metamodels for expensive simulations",
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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Monotonicity-preserving bootstrapped kriging metamodels for expensive simulations. / Kleijnen, Jack P.C.; van Beers, W.C.M.

In: The Journal of the Operational Research Society, Vol. 64, No. 5, 2013, p. 708-717.

Research output: Contribution to journalArticleScientificpeer-review

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