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Bayesian Estimation and Prediction for Inhomogeneous Spatiotemporal Log-Gaussian Cox Processes Using Low-Rank Models, With Application to Criminal Surveillance

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  • Alexandre Rodrigues
  • Peter J. Diggle

Abstract

In this article, we propose a method for conducting likelihood-based inference for a class of nonstationary spatiotemporal log-Gaussian Cox processes. The method uses convolution-based models to capture spatiotemporal correlation structure, is computationally feasible even for large datasets, and does not require knowledge of the underlying spatial intensity of the process. We describe an application to a surveillance system for detecting emergent spatiotemporal clusters of homicides in Belo Horizonte, Brazil, and discuss the advantages and drawbacks of our model-based approach by comparison with other spatiotemporal surveillance methods that have been proposed in the literature.

Suggested Citation

  • Alexandre Rodrigues & Peter J. Diggle, 2012. "Bayesian Estimation and Prediction for Inhomogeneous Spatiotemporal Log-Gaussian Cox Processes Using Low-Rank Models, With Application to Criminal Surveillance," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 93-101, March.
    • Handle: RePEc:taf:jnlasa:v:107:y:2012:i:497:p:93-101
    DOI: 10.1080/01621459.2011.644496
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    References listed on IDEAS

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    1. Peter A. Rogerson, 2001. "Monitoring point patterns for the development of space–time clusters," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 164(1), pages 87-96.
    2. Martin Kulldorff, 2001. "Prospective time periodic geographical disease surveillance using a scan statistic," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 164(1), pages 61-72.
    3. Christian Sonesson & David Bock, 2003. "A review and discussion of prospective statistical surveillance in public health," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 166(1), pages 5-21, February.
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    Cited by:

    1. Kajita, Mami & Kajita, Seiji, 2020. "Crime prediction by data-driven Green’s function method," International Journal of Forecasting, Elsevier, vol. 36(2), pages 480-488.

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