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Modelling Burglary in Chicago using a self-exciting point process with isotropic triggering

Part of: Markov processes Mathematical sociology Probabilistic methods, simulation and stochastic differential equations

Published online by Cambridge University Press:  08 April 2021

CRAIG GILMOUR  and
DESMOND J. HIGHAM
CRAIG GILMOUR
Affiliation:
Department of Mathematics and Statistics, University of Strathclyde, Glasgow, G1 1XH, UK email: cgilmour23@gmail.com
DESMOND J. HIGHAM
Affiliation:
School of Mathematics, University of Edinburgh, Edinburgh, EH9 3FD, UK email: d.j.higham@ed.ac.uk
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Abstract

Self-exciting point processes have been proposed as models for the location of criminal events in space and time. Here we consider the case where the triggering function is isotropic and takes a non-parametric form that is determined from data. We pay special attention to normalisation issues and to the choice of spatial distance measure, thereby extending the current methodology. After validating these ideas on synthetic data, we perform inference and prediction tests on public domain burglary data from Chicago. We show that the algorithmic advances that we propose lead to improved predictive accuracy.

Keywords

Hawkes processcriminologynon-parametrichotspots

MSC classification

Primary: 65C20: Models, numerical methods
Secondary: 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) 91D99: None of the above, but in this section
Type
Papers
Information
European Journal of Applied Mathematics , Volume 33 , Issue 2 , April 2022 , pp. 369 - 391
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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Footnotes

*

Supported by EPSRC Programme Grant EP/P020720/1.

†

Supported by grant EP/M00158X/1 from the EPSRC/RCUK Digital Economy Programme and by EPSRC Programme Grant EP/P020720/1.

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