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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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    References listed on IDEAS

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    Cited by:

    1. Racek, Daniel & Thurner, Paul & Kauermann, Goeran, 2024. "Integrating Spatio-temporal Diffusion into Statistical Forecasting Models of Armed Conflict via Non-parametric Smoothing," OSF Preprints q59dr, Center for Open Science.
    2. Chiang, Wen-Hao & Liu, Xueying & Mohler, George, 2022. "Hawkes process modeling of COVID-19 with mobility leading indicators and spatial covariates," International Journal of Forecasting, Elsevier, vol. 38(2), pages 505-520.
    3. John Leverso & Youness Diouane & George Mohler, 2025. "Measuring Online–Offline Spillover of Gang Violence Using Bivariate Hawkes Processes," Journal of Quantitative Criminology, Springer, vol. 41(1), pages 103-131, March.
    4. 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.
    5. Andrew P. Wheeler & Wouter Steenbeek, 2021. "Mapping the Risk Terrain for Crime Using Machine Learning," Journal of Quantitative Criminology, Springer, vol. 37(2), pages 445-480, June.
    6. 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.
    7. 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).
    8. repec:osf:osfxxx:q59dr_v1 is not listed on IDEAS

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