In this paper, we further investigate the problem of selecting a set of design points for universal kriging, which is a widely used technique for spatial data analysis. Our goal is to select the design points in order to make simultaneous predictions of the random variable of interest at a finite number of unsampled locations with maximum precision. Specifically, we consider as response a correlated random field given by a linear model with an unknown parameter vector and a spatial error correlation structure. We propose a new design criterion that aims at simultaneously minimizing the variation of the prediction errors at various points. We also present various efficient techniques for incrementally building designs for that criterion scaling well for high dimensions. Thus the method is particularly suitable for big data applications in areas of spatial data analysis such as mining, hydrogeology, natural resource monitoring, and environmental sciences or equivalently for any computer simulation experiments. We have demonstrated the effectiveness of the proposed designs through two illustrative examples: one by simulation and another based on real data from Upper Austria.

在本文中，我们进一步研究了为通用克里金法选择一组设计点的问题，通用克里金法是一种广泛使用的空间数据分析技术。我们的目标是选择设计点，以便以最大精度同时预测有限数量的未采样位置处的感兴趣的随机变量。具体来说，我们将由具有未知参数向量和空间误差相关结构的线性模型给出的相关随机场视为响应。我们提出了一种新的设计标准，旨在同时最小化不同点的预测误差的变化。我们还提出了各种有效的技术，用于逐步构建符合高维度标准的设计。因此，该方法特别适合于空间数据分析领域的大数据应用，例如采矿、水文地质学、自然资源监测和环境科学或等同于任何计算机模拟实验。我们通过两个说明性示例证明了所提出的设计的有效性：一个是模拟，另一个基于上奥地利州的真实数据。