  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.
