Journal Article

Crime risk assessment through Cox and self-exciting spatio-temporal point processes

Angulo, José M., Choiruddin, Achmad, Escudero, Isabel, Mateu, Jorge

2025

Overview

Crime risk assessment needs tackling complex interrelationships between stochastic and deterministic components of spatio-temporal models. Criminal phenomena can be modeled using spatio-temporal point patterns of certain criminal data, and here we pay attention to the stochastic models of log-Gaussian Cox processes (LGCP) and self-exciting Hawkes processes (SEHP). We provide a comprehensive modeling strategy, combining both processes, noting that: (a) an LGCP facilitates the incorporation of first-order information through spatial and temporal deterministic components and second-order information through a stochastic component, and (b) a SEHP provides sufficient flexibility to incorporate various components in the background subprocess. To account for crime risk assessment, the deterministic components of the LGCP were estimated using a generalized linear model (GLM) for the temporal part, and a generalized additive model with B-splines for the highly nonlinear spatial covariates. In addition, the background rate components of the SEHP were estimated by a non-parametric stochastic reconstruction technique that includes a temporal periodicity, a separable spatial component, a long-term trend, and a semi-parametric method for the relaxation coefficients. MCMC-MALA and maximum likelihood were used for inference in both the LGCP and SEHP processes. We analyze crime events from the city of Riobamba (Ecuador), and with a complementary use of both stochastic point process models, we are able to assess the risk of crime, and provide reliable forecasts for weeks ahead.

• Publisher: Springer Berlin Heidelberg,Springer Nature B.V
• Subject: Aquatic Pollution / Chemistry and Earth Sciences / Computational Intelligence / Computer Science / Crime / Earth and Environmental Science / Earth Sciences / Environment / Gaussian process / Generalized linear models / Math. Appl. in Environmental Science / Original Paper / Periodicity / Physics / Probability Theory and Stochastic Processes / Risk assessment / Spatiotemporal data / Statistical models / Statistics for Engineering / Stochastic models / Stochastic processes / Waste Water Technology / Water Management / Water Pollution Control