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.

翻译：本文进一步研究了通用克里金方法中设计点的选择问题，该方法广泛应用于空间数据分析。我们的目标是通过选择设计点，以最大精度在有限个未采样位置对感兴趣的随机变量进行同时预测。具体而言，我们将响应视为由带未知参数向量的线性模型和空间误差相关结构给出的相关随机场。我们提出了一种新的设计准则，旨在同时最小化不同点处预测误差的变异性。同时，我们提出了多种高效技术，用于针对该准则逐步构建设计，这些技术在高维场景下具有良好的可扩展性。因此，该方法特别适用于空间数据分析领域（如采矿、水文地质、自然资源监测和环境科学）中的大数据应用，或等效于任何计算机模拟实验。通过两个示例（一个基于模拟，另一个基于奥地利上奥地利州的真实数据）验证了所提设计的有效性。