  There is significant interest in being able to predict where crimes will
happen, for example to aid in the efficient tasking of police and other
protective measures. We aim to model both the temporal and spatial dependencies
often exhibited by violent crimes in order to make such predictions. The
temporal variation of crimes typically follows patterns familiar in time series
analysis, but the spatial patterns are irregular and do not vary smoothly
across the area. Instead we find that spatially disjoint regions exhibit
correlated crime patterns. It is this indeterminate inter-region correlation
structure along with the low-count, discrete nature of counts of serious crimes
that motivates our proposed forecasting tool. In particular, we propose to
model the crime counts in each region using an integer-valued first order
autoregressive process. We take a Bayesian nonparametric approach to flexibly
discover a clustering of these region-specific time series. We then describe
how to account for covariates within this framework. Both approaches adjust for
seasonality. We demonstrate our approach through an analysis of weekly reported
violent crimes in Washington, D.C. between 2001-2008. Our forecasts outperform
standard methods while additionally providing useful tools such as prediction
intervals.
