On Prediction Properties of Kriging: Uniform Error Bounds and Robustness
On Prediction Properties of Kriging: Uniform Error Bounds and Robustness
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DOI：
10.1080/01621459.2019.1598868
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发表时间：
2017-10
影响因子：
3.7
通讯作者：
Wenjia Wang;Rui Tuo;C. F. Jeff Wu
中科院分区：
文献类型：
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作者：
Wenjia Wang;Rui Tuo;C. F. Jeff Wu
摘要基于高斯随机场的Kriging算法在未知函数重构中得到了广泛的应用。克里金方法具有点向预测分布，计算简单。然而，在许多应用中，人们希望同时预测一系列未尝试过的点。在此工作中，我们得到了在一致度量下的简单通用克里格预测器的一些误差界。它适用于任意维度的分散输入点集，也适用于高斯过程协方差函数指定错误的情况。这些结果有助于更好地理解kriging在高斯或mat<s:1>相关函数下的收敛速度，空间填充设计与kriging模型之间的关系，以及mat<s:1>相关函数的鲁棒性。本文的补充材料可在网上获得。
Abstract Kriging based on Gaussian random fields is widely used in reconstructing unknown functions. The kriging method has pointwise predictive distributions which are computationally simple. However, in many applications one would like to predict for a range of untried points simultaneously. In this work, we obtain some error bounds for the simple and universal kriging predictor under the uniform metric. It works for a scattered set of input points in an arbitrary dimension, and also covers the case where the covariance function of the Gaussian process is misspecified. These results lead to a better understanding of the rate of convergence of kriging under the Gaussian or the Matérn correlation functions, the relationship between space-filling designs and kriging models, and the robustness of the Matérn correlation functions. Supplementary materials for this article are available online.