Bayesian Variable Selection for Censored Spatial Responses with Application to PFAS Concentrations in California

Abstract

Per- and polyfluoroalkyl substances (PFAS) are persistent environmental pollutants of major public health concern due to their resistance to degradation, widespread presence, and potential health risks. Analyzing PFAS in groundwater is challenging due to left-censoring and strong spatial dependence. Although PFAS levels are influenced by sociodemographic, industrial, and environmental factors, the relative importance of these drivers remains unclear, highlighting the need for robust statistical tools to identify key predictors from a large candidate set. We present a Bayesian hierarchical framework that integrates censoring into a spatial process model via approximate Gaussian processes and employs a global-local shrinkage prior for high-dimensional variable selection. We evaluate three post-selection strategies, namely, credible interval rules, shrinkage weight thresholds, and clustering-based inclusion and compare their performance in terms of predictive accuracy, censoring robustness, and variable selection stability through cross-validation. Applied to PFOS concentrations in California groundwater, the model identifies a concise, interpretable set of predictors, including demographic composition, industrial facility counts, proximity to airports, traffic density, and environmental features such as herbaceous cover and elevation. These findings demonstrate that the proposed approach delivers stable, interpretable inference in censored, spatial, high-dimensional contexts, thereby offering actionable insights into the environmental and industrial factors affecting PFAS concentrations.