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 buillding 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. The effectiveness of the proposed designs is demonstrated through numerical examples.

翻译：本文进一步研究了通用克里金方法中设计点集选择问题，该方法是空间数据分析的常用技术。我们的目标是通过选择设计点，以最大精度对有限个未采样位置的感兴趣随机变量进行同步预测。具体而言，我们将响应视为由未知参数向量的线性模型与空间误差相关结构共同确定的关联随机场。本文提出一种新的设计准则，旨在同步最小化各位置预测误差的变异。我们还提出了多种适用于该准则的高效增量式构造技术，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、自然资源监测及环境科学）中的大数据应用，或任何计算机模拟实验。通过数值算例验证了所提设计方法的有效性。