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.

Keywords:

• simulation
• sensitivity analysis
• Kriging
• bootstrapping
• queueing

Electronic supplementary material

The online version of this article (doi:10.1057/jors.2011.148) contains supplementary material, which is available to authorized users.

Supplementary Information accompanies the paper on Journal of the Operational Research Society website (http://www.palgrave-journals.com/jors/)

Electronic supplementary material

The online version of this article (doi:10.1057/jors.2011.148) contains supplementary material, which is available to authorized users.

Supplementary Information accompanies the paper on Journal of the Operational Research Society website (http://www.palgrave-journals.com/jors/)

Acknowledgements

We thank two (anonymous) referees and Dick den Hertog (Tilburg University) for their comments on earlier versions, which lead to drastic revisions.