Abstract
The self-exciting point process (SEPP) is a model of the spread of crime in space and time, incorporating background and triggering processes. It shows promising predictive performance and forms the basis of a popular commercial software package, however few detailed case studies describing the application of the SEPP to crime data exist in the scientific literature. Using open crime data from the City of Chicago, USA, we apply the SEPP to crime prediction of assaults and burglaries in nine distinct geographical regions of the city. The results indicate that the algorithm is not robust to certain features of the data, generating unrealistic triggering functions in various cases. A simulation study is used to demonstrate that this outcome is associated with a reduction in predictive accuracy. Analysing the second-order spatial properties of the data demonstrates that the failures in the algorithm are correlated with anisotropy. A modified version of the SEPP model is developed in which triggering is non-directional. We show that this provides improved robustness, both in terms of the triggering structure and the predictive accuracy.
Highlights
The ability to predict the future location of crime hotspots confers myriad advantages on a police force, including planning effective proactive interventions, reducing the Electronic supplementary material The online version of this article contains supplementary material, which is available to authorized users
Despite the fact that this software is currently used in various police forces in the USA, to our knowledge there are only two detailed case studies in the scientific literature describing the application of the self-exciting point process (SEPP) to crime data (Mohler et al 2011; Mohler 2014)
Since the triggering component of the SEPP model considers the links between pairs of crimes, we focus on the second-order properties of the crime datasets
Summary
The ability to predict the future location of crime hotspots confers myriad advantages on a police force, including planning effective proactive interventions, reducing the Electronic supplementary material The online version of this article (doi:10.1007/s12061-016-9198-y) contains supplementary material, which is available to authorized users. The self-exciting point process (SEPP) model is a recentlydeveloped crime prediction method whose inputs are the locations and times of historic crimes It achieves strong predictive performance when applied to a residential burglary dataset from Los Angeles, USA (Mohler et al 2011). The SEPP is an approach based on a theoretical model that was originally developed in the context of interpreting seismic activity (Musmeci and Vere-Jones 1992), but was recently applied to crime prediction by Mohler et al (Mohler et al 2011). Mohler et al (2011) use an expectation-maximisation (EM) algorithm and kernel density estimates (KDEs) to achieve this task This approach is theoretically more flexible, since it does not require any prior assumptions on the functional form of the background and triggering functions. Initialisation of P is performed by assuming a simple triggering form that is exponentially decaying in time and bivariate normal in space: pij ÀÀ exp −α t j
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