Improving social harm indices with a modulated Hawkes process

Communities are affected adversely by a range of social harm events, such as crime, traffic crashes, medical emergencies, and drug use. The police, fire, health and social service departments are tasked with mitigating such social harm through various types of interventions. While various different social harm indices have been proposed for allocating resources to spatially fixed hotspots, the risk of social harm events is dynamic, and new algorithms and software systems that are capable of quickly identifying risks and triggering appropriate public safety responses are needed. We propose a novel modulated Hawkes process for this purpose that offers flexible approaches to both (i) the incorporation of spatial covariates and leading indicators for variance reduction in the case of rarer event categories, and (ii) the capture of dynamic hotspot formation through self-excitation. We present an efficient l1-penalized EM algorithm for estimating the model that performs feature selection for the spatial covariates of each incident type simultaneously. We provide simulation results using data from the Indianapolis Metropolitan Police Department in order to illustrate the advantages of the modulated Hawkes process model of social harm over various recently introduced social harm indices and property crime Hawkes processes.