Spatial boundary detection for areal counts

Abstract

Two Bayesian nonparametric model-based approaches to areal boundary detection for count outcomes are proposed, compared, and illustrated. The linear predictor in a standard Poisson regression is augmented with random effects stemming from modified stick-breaking representations of the Dirichlet process. The modifications induce spatial correlation among counts from differing counties such that closer counties are more highly correlated. The discrete nature of the Dirichlet process is an advantage in this setting as two counties can have the same random effect, implying no boundary, with positive probability. The methods are compared on counts of patients hospitalized due to pneumonia and influenza in Minnesota.