Abstract: With increasing accessibility to Geographical Information Systems (GIS) software, researchers and administrators in public health routinely encounter areal data compiled as aggregates over areal regions, such as counts or rates across counties in a state. Spatial models for areal data attempt to deliver smoothed maps by accounting for high variability in certain regions. Subsequently, inferential interest is focused upon formally identifying the “difference edges” or “ difference boundaries” on the map that delineate adjacent regions with vastly disparate outcomes, perhaps caused by latent risk factors. We propose nonparametric Bayesian models for areal data that can formally identify boundaries between disparate neighbors. After elucidating these models and their estimation methods, we resort to simulation experiments to assess their effectiveness, and subsequently analyze Pneumonia and Influenza hospitalization maps from the SEER-Medicare program in Minnesota, where we detect and report highly disparate neighboring counties.

Key words and phrases: Areal data, conditional autoregressive model, difference boundary, Dirichlet process, stick-breaking process, wombling.