Nonstationary Gaussian Process Models Using Spatial Hierarchical Clustering from Finite Differences

Analysis of these large spatial datasets for scientific inquiry is typically carried out using the Gaussian process. However, nonstationary behavior and computational requirements for large spatial datasets can prohibit efficient implementation of Gaussian process models.

To perform computationally feasible inference for large spatial data, we consider partitioning a spatial region into disjoint sets using hierarchical clustering of observations and finite differences as a measure of dissimilarity. Intuitively, directions with large finite differences indicate directions of rapid increase or decrease and are, therefore, appropriate for partitioning the spatial region. Spatial contiguity of the resulting clusters is enforced by only clustering Voronoi neighbors.