An adaptive two-stage dual metamodeling approach for stochastic simulation experiments

In this article we propose an adaptive two-stage dual metamodeling approach for stochastic simulation experiments, aiming at exploiting the benefits of fitting the mean and variance function models simultaneously to improve the predictive performance of Stochastic Kriging (SK). To this end, we study the effects of replacing the sample variances with smoothed variance estimates on the predictive performance of SK, articulate the links between SK and least-squares support vector regression, and provide some useful data-driven methods for identifying important design points. We argue that efficient data-driven experimental designs for stochastic simulation metamodeling can be “learned” through a “dense and shallow” initial design (i.e., relatively many design points with relatively little effort at each), and efficient budget allocation rules can be seamlessly incorporated into the proposed approach to intelligently spend the remaining simulation budget on the important design points identified. Two numerical examples are provided to demonstrate the promise held by the proposed approach in providing highly accurate mean response surface approximations.