Statistical Modelling 24 (2) (2024), 139–168
Self-exciting point process modelling of crimes on
linear networks
Nicoletta D’Angelo,
Department of Economics,
Business and Statistics,
University of Palermo,
Sicily,
Italy.
e-mail: nicoletta.dangelo@unipa.it
David Payares,
Department of Earth Observation Science,
University of Twente,
Overijssel,
Netherlands.
Giada Adelfio,
Department of Economics,
Business and Statistics,
University of Palermo,
Sicily,
Italy.
Jorge Mateu,
Department of Mathematics,
Universitat Jaume I,
Valencian Community,
Spain.
Abstract:
Although there are recent developments for the analysis of first and second-order characteristics
of point processes on networks, there are very few attempts in introducing models for network
data. Motivated by the analysis of crime data in Bucaramanga (Colombia), we propose a spatiotemporal
Hawkes point process model adapted to events living on linear networks. We first consider
a non-parametric modelling strategy, for which we follow a non-parametric estimation of both the
background and the triggering components. Then we consider a semi-parametric version, including a
parametric estimation of the background based on covariates, and a non-parametric one of the triggering
effects. Our model can be easily adapted to multi-type processes. Our network model outperforms
a planar version, improving the fitting of the self-exciting point process model.
Keywords:
covariates, crime data, Hawkes processes, linear networks, self-exciting point processes,
spatio-temporal point processes
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