Burglary in London: Insights from Statistical Heterogeneous Spatial Point Processes

TL;DR

This paper introduces a Bayesian spatial mixture model to analyze burglary patterns in London, accounting for local variations and spatial dependence, providing operational insights into criminal behavior.

Contribution

It develops a novel spatial extension to mixture modeling for crime data, incorporating spatial dependence and local covariate effects with a Bayesian framework.

Findings

Identifies localized effects of covariates on burglary intensity.

Models spatial dependence between nearby locations.

Provides a Python implementation for practical use.

Abstract

To obtain operational insights regarding the crime of burglary in London we consider the estimation of effects of covariates on the intensity of spatial point patterns. By taking into account localised properties of criminal behaviour, we propose a spatial extension to model-based clustering methods from the mixture modelling literature. The proposed Bayesian model is a finite mixture of Poisson generalised linear models such that each location is probabilistically assigned to one of the clusters. Each cluster is characterised by the regression coefficients which we subsequently use to interpret the localised effects of the covariates. Using a blocking structure of the study region, our approach allows specifying spatial dependence between nearby locations. We estimate the proposed model using Markov Chain Monte Carlo methods and provide a Python implementation.