A hierarchical approach to scalable Gaussian process regression for spatial data

Large scale and highly detailed geospatial datasets currently offer rich opportunities for empirical investigation, where finer-level investigation of spatial spillovers and spatial infill can now be done at the parcel level. Gaussian process regression (GPR) is particularly well suited for such investigations, but is currently limited by its need to manipulate and store large dense covariance matrices. The central purpose of this paper is to develop a more efficient version of GPR based on the hierarchical covariance approximation proposed by Chen et al. (J Mach Learn Res 18:1–42, 2017) and Chen and Stein (Linear-cost covariance functions for Gaussian random fields, arXiv:1711.05895, 2017). We provide a novel probabilistic interpretation of Chen’s framework, and extend his method to the analysis of local marginal effects at the parcel level. Finally, we apply these tools to a spatial dataset constructed from a 10-year period of Oklahoma County Assessor databases. In this setting, we are able to identify both regions of possible spatial spillovers and spatial infill, and to show more generally how this approach can be used for the systematic identification of specific development opportunities.