A criterion and incremental design construction for simultaneous kriging predictions

TL;DR

This paper introduces a new design criterion and incremental construction method for universal kriging that enhances simultaneous prediction accuracy at multiple locations, especially useful for large spatial datasets.

Contribution

It proposes a novel criterion for design point selection in universal kriging and efficient incremental algorithms suitable for high-dimensional, big data spatial analysis.

Findings

Effective design methods demonstrated through simulation.

Successful application to real data from Upper Austria.

Improved prediction precision at multiple locations.

Abstract

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.