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（一种广泛用于空间数据分析的技术）中设计点集选择的问题。我们的目标是选择设计点，以便在有限个未采样位置上对感兴趣随机变量进行联合预测时达到最大精度。具体而言，我们将响应视为由带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。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。我们还提出了多种高效技术，用于针对该准则增量式构建设计，这些技术在高维情况下具有良好的扩展性。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）的大数据应用，或任何计算机仿真实验。我们通过两个实例（一个基于仿真，另一个基于奥地利上奥地利州的真实数据）展示了所提出设计的有效性。