On the Choice of Nugget in Kriging Modeling for Deterministic Computer Experiments
On the Choice of Nugget in Kriging Modeling for Deterministic Computer Experiments
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DOI：
10.1080/10618600.2012.738961
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发表时间：
2014-01
影响因子：
2.4
通讯作者：
Chien‐Yu Peng;WU C.F.Jeff;C. Peng;WU C.F.J.
中科院分区：
文献类型：
--
作者：
Chien‐Yu Peng;WU C.F.Jeff;C. Peng;WU C.F.J.
克里金法通常用于开发模拟器作为计算密集型模拟的替代方法。克里金法的一大困难是协方差矩阵的逆计算中潜在的数值不稳定，这可能导致克里金预测器的较大变异性和较差的性能。首先，我们研究克里格法中病态的一些原因。然后我们研究了在克里金法中使用块金来克服数值不稳定性。给出了插值偏差和均方预测误差的一些渐近结果。最后，我们研究基于一些代数下界的块金参数的选择和正则化迹的使用。进行了模拟研究，以显示有核金和无核金的克里金法之间的差异，并证明前者的优点。本文有网上的补充材料。
Kriging is commonly used for developing emulators as surrogates for computationally intensive simulations. One difficulty with kriging is the potential numerical instability in the computation of the inverse of the covariance matrix, which can lead to large variability and poor performance of the kriging predictor. First, we study some causes of ill-conditioning in kriging. We then study the use of nugget in kriging to overcome the numerical instability. Some asymptotic results on its interpolation bias and mean squared prediction errors are presented. Finally, we study the choice of the nugget parameter based on some algebraic lower bounds and use of a regularizing trace. A simulation study is performed to show the differences between kriging with and without nugget and to demonstrate the advantages of the former. This article has supplementary materials online.