Optimal Policy Learning Under Spatial Dependence With Applications to Groundwater in Wisconsin

Music City Center 

When installing drinking water wells, it's well-understood that increasing well depth improves the quality of the groundwater, but also raises costs. Policymakers must therefore determine the minimum well depth required to meet the public health standards for contaminants in groundwater, such as nitrates, a popular contaminant from fertilizers. In Wisconsin, the current approach to setting the minimum well depth is often a single, static number, which ignores the local hydrogeological characteristics. In this paper, we propose a data-driven method for estimating the Spatial Minimum Resource Threshold Policy (spMRTP), which determines the minimum treatment level needed at each location to meet the target outcome. A key feature of spMRTP is to account for spatial dependence of contaminants where high contaminants levels in one area often imply high contaminant levels in adjacent areas. We estimate spMRTP by empirical risk minimization with a novel, nonparametric, doubly robust loss function. For computation, we propose to use the Vecchia approximation to efficiently evaluate the minimizer. Our simulation results demonstrate that the proposed method outperforms competing approaches, including non-spatial methods for policy learning and indirect estimation methods. We also apply our method to water quality data collected from 2014 to 2024 in Wisconsin and generate a spatial map of optimal, minimum well depths in Wiscnosin to meet the 10-ppm public health standard for nitrates.

Transportability

Overlap condition

Density ratio

Poisson regression

Inhomogeneous Poisson point process 

Health Policy Statistics Section