A Discrete Kernel Stick-Breaking Model for Detecting Spatial Boundaries in Hydraulic Fracturing Wastewater Disposal Well Placement Across Ohio

Abstract

Detecting sharp differences, or boundaries, in areal data can uncover important biological, physical and/or social differences between spatial regions. We introduce a new discrete areal data kernel function for use in the kernel stick‐breaking process framework that is shown to yield improved (i) detection of spatial boundaries, (ii) estimation of regression parameters and (iii) model fit through a simulation study and comparison with existing approaches. We use the model to analyse county‐level hydraulic fracturing Class II injection well counts in Ohio, where interesting boundary patterns may exist due to the close connection between hydraulic fracturing and shale rock formations. Class II injection wells are used for disposing hydraulic fracturing liquid waste and may pose an environmental risk for surrounding communities. Counties located on the Devonian shale with increased poverty, less income equality, smaller proportion of the population that is white, and increased population density are found to contain more wells, with the relationship reversed for counties off the shale. Results suggest that the new method provides improved model fit and is robust to the exclusion of an important spatially varying covariate, while also detecting boundaries surrounding different shale rock formations. The method is implemented in the R package KSBound.