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Burglary in London: insights from statistical heterogeneous spatial point processes

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  • Jan Povala
  • Seppo Virtanen
  • Mark Girolami

Abstract

To obtain operational insights regarding the crime of burglary in London, we consider the estimation of the effects of covariates on the intensity of spatial point patterns. Inspired by localized properties of criminal behaviour, we propose a spatial extension to mixtures of generalized linear models from the mixture modelling literature. The Bayesian model proposed is a finite mixture of Poisson generalized linear models such that each location is probabilistically assigned to one of the groups. Each group is characterized by the regression coefficients, which we subsequently use to interpret the localized effects of the covariates. By using a blocks structure of the study region, our approach enables specifying spatial dependence between nearby locations. We estimate the proposed model by using Markov chain Monte Carlo methods and we provide a Python implementation.

Suggested Citation

  • Jan Povala & Seppo Virtanen & Mark Girolami, 2020. "Burglary in London: insights from statistical heterogeneous spatial point processes," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(5), pages 1067-1090, November.
    • Handle: RePEc:bla:jorssc:v:69:y:2020:i:5:p:1067-1090
    DOI: 10.1111/rssc.12431
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    References listed on IDEAS

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    3. Carmen Fernández & Peter J. Green, 2002. "Modelling spatially correlated data via mixtures: a Bayesian approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 805-826, October.
    4. Danilo Alvares & Carmen Armero & Anabel Forte, 2018. "What Does Objective Mean in a Dirichlet†multinomial Process?," International Statistical Review, International Statistical Institute, vol. 86(1), pages 106-118, April.
    5. Gelfand A.E. & Kim H-J. & Sirmans C.F. & Banerjee S., 2003. "Spatial Modeling With Spatially Varying Coefficient Processes," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 387-396, January.
    6. Green P.J. & Richardson S., 2002. "Hidden Markov Models and Disease Mapping," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1055-1070, December.
    7. Taddy, Matthew A., 2010. "Autoregressive Mixture Models for Dynamic Spatial Poisson Processes: Application to Tracking Intensity of Violent Crime," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1403-1417.
    8. Mark Girolami & Ben Calderhead, 2011. "Riemann manifold Langevin and Hamiltonian Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(2), pages 123-214, March.
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