TITLE: Bayesian Nonparametric Analysis of Spatial Variation with Discontinuities
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Abstract: Spatial data often display high levels of smoothness but can simultaneously present abrupt discontinuities, especially in urban environments. We model neighborhood crime trends over time in the City of Philadelphia by combining a spatial local shrinkage model with spatial partitions of areal units to allow for discontinuities. We explore two challenges that arise in this setting.   First, the vast space of spatial partitions makes typical stochastic search techniques computationally prohibitive. We introduce an ensemble optimization procedure that summarizes the posterior by simultaneously targeting several high probability partitions.   Second, the areal units are organized in a hierarchical structure that has multiple resolution levels. We introduce a model which combines the Nested Dirichlet Process with the Hierarchical Dirichlet Process to allow for flexible partitions of both high- and low-resolution areal units.   Both our methods are demonstrated on synthetic data and on real data in Philadelphia.