A mechanistic bivariate point process model for crime pattern analysis

Abstract

The statistical analysis of crime data has gained attention in the last decade. In particular, the availability of spatio-temporal crime data at the event level allows us to model the incidence of crime with high precision. Point process models are the natural tool to study crime patterns. As it is well-known that crime events often spread as a contagion process, mechanistic self-exciting models are usually considered in this context. In this paper, we propose a mechanistic bivariate spatio-temporal model for the first-order intensity function of the point processes associated with the intensity of two crime types. Specifically, the model includes separate estimates of the overall temporal and spatial intensities of crime and a spatio-temporal interaction term for each of the crime types under analysis. Regarding the spatio-temporal term, we model how the occurrence of previous crime events (from any of the two types) influences the intensity of each type of crime under study. We consider a dataset of crime events recorded in Valencia (Spain) during the year 2017 and focus on two crime types for the analysis: property crime and robbery. The results show that there is an association between the recent occurrence of either property crimes or robberies and the intensity of both crime types. Several spatio-temporal monitoring tools are described and discussed as well.