All Times ET
Keywords: Constrained domains, Directed Acyclic Graphs, Groundwater contamination, Scalable Gaussian Process, Spatial statistics
Providing safe drinking water is a globally imperative issue. In order to do so, it is necessary to properly understand the spatial distribution of aqueous pollutants in groundwater, since many water systems use groundwater resources. One of the distinguishable characteristics of pollutants in groundwater from those in air is that the measurements are collected and meaningful only in a constrained domain, i.e., groundwater bodies with intrinsic geometry. Typical spatial Gaussian Process (GP) models ignore the unique geometry of the domain, which may lead to inappropriate smoothing over physical barriers. We focus on developing a scalable GP method that incorporates the constrained domain, motivated by modeling of spatial variability of pollutants in groundwater.
One way to construct a scalable GP model is via sparsity-inducing directed acyclic graphs (DAGs). The sparsity-inducing DAGs limit neighbors to receive graph edges from and impose conditional independence to the rest given the neighbors. A main contribution of this paper is the development of the Barrier Overlap-Removal Acyclic Directed Graph GP (BORA-GP) that constructs neighbors conforming to physical barriers. It removes an edge in a DAG if a linear path between two points overlaps the barriers, which enables characterization of dependence in constrained domains. Since BORA-GP is a well-defined spatial process, we embed it into scalable Bayesian spatial process models, accounting for local geometries. We illustrate performance gains relative to existing methods through simulations and analyze water pollutant measurements in California collected through the Groundwater Ambient Monitoring and Assessment Program (GAMA).