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Self‐exciting point processes with spatial covariates: modelling the dynamics of crime

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  • Alex Reinhart
  • Joel Greenhouse

Abstract

Crime has both varying patterns in space, related to features of the environment, economy and policing, and patterns in time arising from criminal behaviour, such as retaliation. Serious crimes may also be presaged by minor crimes of disorder. We demonstrate that these spatial and temporal patterns are generally confounded, requiring analyses to take both into account, and propose a spatiotemporal self‐exciting point process model that incorporates spatial features, near repeat and retaliation effects, and triggering. We develop inference methods and diagnostic tools, such as residual maps, for this model, and through extensive simulation and crime data obtained from Pittsburgh, Pennsylvania, demonstrate its properties and usefulness.

Suggested Citation

  • Alex Reinhart & Joel Greenhouse, 2018. "Self‐exciting point processes with spatial covariates: modelling the dynamics of crime," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 67(5), pages 1305-1329, November.
    • Handle: RePEc:bla:jorssc:v:67:y:2018:i:5:p:1305-1329
    DOI: 10.1111/rssc.12277
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    2. Rummens, Anneleen & Hardyns, Wim, 2021. "The effect of spatiotemporal resolution on predictive policing model performance," International Journal of Forecasting, Elsevier, vol. 37(1), pages 125-133.
    3. Giada Adelfio & Marcello Chiodi, 2021. "Including covariates in a space-time point process with application to seismicity," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(3), pages 947-971, September.
    4. Grames, Eliza M. & Stepule, Piper L. & Herrick, Susan Z. & Ranelli, Benjamin T. & Elphick, Chris S., 2022. "Separating acoustic signal into underlying behaviors with self-exciting point process models," Ecological Modelling, Elsevier, vol. 468(C).

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