Burglary in London: insights from statistical heterogeneous spatial point processes

To obtain operational insights regarding the crime of burglary in London, we consider the estimation of the effects of covariates on the intensity of spatial point patterns. Inspired by localized properties of criminal behaviour, we propose a spatial extension to mixtures of generalized linear models from the mixture modelling literature. The Bayesian model proposed is a finite mixture of Poisson generalized linear models such that each location is probabilistically assigned to one of the groups. Each group is characterized by the regression coefficients, which we subsequently use to interpret the localized effects of the covariates. By using a blocks structure of the study region, our approach enables specifying spatial dependence between nearby locations. We estimate the proposed model by using Markov chain Monte Carlo methods and we provide a Python implementation.