Bayesian Network Regularized Regression for Modeling Urban Crime Occurrences

Abstract

Analyses of occurrences of residential burglary in urban areas have shown that crime rates are not spatially homogeneous: rates vary across the network of city streets, resulting in some areas being far more susceptible to crime than others. The explanation for why a certain segment of the city experiences high crime may be different than why a neighboring area experiences high crime. Motivated by the importance of understanding spatial patterns such as these, we consider a statistical model of burglary defined on the street network of Boston, Massachusetts. Leveraging ideas from functional data analysis, our proposed solution consists of a generalized linear model with vertex-indexed covariates, allowing for an interpretation of the covariate effects at the street level. We employ a regularization procedure cast as a prior distribution on the regression coefficients under a Bayesian setup, so that the predicted responses vary smoothly according to the connectivity of the city. We introduce a novel variable selection procedure, examine computationally efficient methods for sampling from the posterior distribution of the model parameters, and demonstrate the flexibility of our proposed modeling structure. The resulting model and interpretations provide insight into the spatial network patterns and dynamics of residential burglary in Boston.