Gradient Extrapolated Stochastic Kriging
Gradient Extrapolated Stochastic Kriging
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DOI：
10.1145/2658995
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发表时间：
2014-08
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影响因子：
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通讯作者：
H. Qu;M. Fu
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作者：
H. Qu;M. Fu
我们引入一种在可获取额外直接梯度信息（例如由微扰分析或似然比方法等技术提供）的情况下增强随机克里金法的方法。这种新方法称为梯度外推随机克里金法（GESK），它通过外推额外的响应来纳入直接梯度估计。对于两种简化情形，我们表明在步长的某些条件下，与随机克里金法相比，GESK降低了均方误差（MSE）。由于外推步长对GESK模型的性能至关重要，我们提出两种不同的方法来确定步长：最大化惩罚似然和最小化积分均方误差。进行了数值实验以说明GESK模型的性能，并将其与其他方法进行比较。
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.