### Monotonicity-preserving bootstrapped Kriging metamodels for expensive simulations

J P C Kleijnen, W C M van Beers
<span title="">2013</span> <i title="Informa UK Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/fq4jrflj6zesjk7f4nb4otuwwy" style="color: black;">Journal of the Operational Research Society</a> </i> &nbsp;
Kriging (Gaussian process, spatial correlation) metamodels approximate the Input/Output (I/O) functions implied by the underlying simulation models; such metamodels serve sensitivity analysis and optimization, especially for computationally expensive simulations. In practice, simulation analysts often know that the I/O function is monotonic. To obtain a Kriging metamodel that preserves this known shape, this article uses bootstrapping (or resampling). Parametric bootstrapping assuming normality
more &raquo; ... may be used in deterministic simulation, but this article focuses on stochastic simulation (including discrete-event simulation) using distribution-free bootstrapping. In stochastic simulation, the analysts should simulate each input combination several times to obtain a more reliable average output per input combination. Nevertheless, this average still shows sampling variation, so the Kriging metamodel does not need to interpolate the average outputs. Bootstrapping provides a simple method for computing a noninterpolating Kriging model. This method may use standard Kriging software, such as the free Matlab toolbox called DACE. The method is illustrated through the M/M/1 simulation model with as outputs either the estimated mean or the estimated 90% quantile; both outputs are monotonic functions of the tra¢ c rate, and have nonnormal distributions. The empirical results demonstrate that monotonicity-preserving bootstrapped Kriging may give higher probability of covering the true simulation output, without lengthening the con...dence interval.
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