  Accurate estimation of the change in crime over time is a critical first step
towards better understanding of public safety in large urban environments.
Bayesian hierarchical modeling is a natural way to study spatial variation in
urban crime dynamics at the neighborhood level, since it facilitates principled
``sharing of information'' between spatially adjacent neighborhoods. Typically,
however, cities contain many physical and social boundaries that may manifest
as spatial discontinuities in crime patterns. In this situation, standard prior
choices often yield overly-smooth parameter estimates, which can ultimately
produce mis-calibrated forecasts. To prevent potential over-smoothing, we
introduce a prior that partitions the set of neighborhoods into several
clusters and encourages spatial smoothness within each cluster. In terms of
model implementation, conventional stochastic search techniques are
computationally prohibitive, as they must traverse a combinatorially vast space
of partitions. We introduce an ensemble optimization procedure that
simultaneously identifies several high probability partitions by solving one
optimization problem using a new local search strategy. We then use the
identified partitions to estimate crime trends in Philadelphia between 2006 and
2017. On simulated and real data, our proposed method demonstrates good
estimation and partition selection performance.
