Time of week intensity estimation from partly interval censored data with applications to police patrol planning

Law enforcement agencies are tasked with crime prevention and crime reduction under limited resources. Having an accurate temporal estimate of the crime rate would be valuable to achieve such a goal. However, estimation is usually complicated by the interval censored nature of crime data. We cast the problem of intensity estimation as a Poisson regression using an EM algorithm to estimate the parameters. Two special penalties are added that provide smoothness over the time of day and day of week. This approach provides accurate intensity estimates and can also uncover day of week clusters that share the same intensity patterns. Both simulated and real crime data gathered from the city of Cincinnati and the city of Dallas are used to demonstrate the effectiveness of the proposed model.