Gradient Extrapolated Stochastic Kriging

We introduce an approach for enhancing stochastic kriging in the setting where additional direct gradient information is available (e.g., provided by techniques such as perturbation analysis or the likelihood ratio method). The new approach, called gradient extrapolated stochastic kriging (GESK), incorporates direct gradient estimates by extrapolating additional responses. For two simplified settings, we show that GESK reduces mean squared error (MSE) compared to stochastic kriging under certain conditions on step sizes. Since extrapolation step sizes are crucial to the performance of the GESK model, we propose two different approaches to determine the step sizes: maximizing penalized likelihood and minimizing integrated mean squared error. Numerical experiments are conducted to illustrate the performance of the GESK model and to compare it with alternative approaches.