Self‐exciting point processes with spatial covariates: modelling the dynamics of crime

Crime has both varying patterns in space, related to features of the environment, economy and policing, and patterns in time arising from criminal behaviour, such as retaliation. Serious crimes may also be presaged by minor crimes of disorder. We demonstrate that these spatial and temporal patterns are generally confounded, requiring analyses to take both into account, and propose a spatiotemporal self-exciting point process model that incorporates spatial features, near repeat and retaliation effects, and triggering. We develop inference methods and diagnostic tools, such as residual maps, for this model, and through extensive simulation and crime data obtained from Pittsburgh, Pennsylvania, demonstrate its properties and usefulness.