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Bayesian dynamic models for space–time point processes

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  • Reis, Edna A.
  • Gamerman, Dani
  • Paez, Marina S.
  • Martins, Thiago G.

Abstract

In this work we propose a model for the intensity of a space–time point process, specified by a sequence of spatial surfaces that evolve dynamically in time. This specification allows flexible structures for the components of the model, in order to handle temporal and spatial variations both separately and jointly. These structures make use of state-space and Gaussian process tools. They are combined to create a richer class of models for the intensity process. This structural approach allows for a decomposition of the intensity into purely temporal, purely spatial and spatio-temporal terms. Inference is performed under a fully Bayesian approach, with the description of simulation-based and analytic methods for approximating the posterior distributions. The proposed methodology is applied to model the incidence of impulses in the small intestine, illustrated by a data-set obtained through an experiment conducted in cats, in order to understand the interaction between the nervous and digestive systems. This application illustrates the usefulness of the proposed methodology and shows it compares favorably against existing alternatives. The paper is concluded with a few directions for further investigation.

Suggested Citation

  • Reis, Edna A. & Gamerman, Dani & Paez, Marina S. & Martins, Thiago G., 2013. "Bayesian dynamic models for space–time point processes," Computational Statistics & Data Analysis, Elsevier, vol. 60(C), pages 146-156.
    • Handle: RePEc:eee:csdana:v:60:y:2013:i:c:p:146-156
    DOI: 10.1016/j.csda.2012.11.008
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    References listed on IDEAS

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    1. Anders Brix & Peter J. Diggle, 2001. "Spatiotemporal prediction for log‐Gaussian Cox processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(4), pages 823-841.
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    5. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    6. Liu, Hua & Brown, Donald E., 2003. "Criminal incident prediction using a point-pattern-based density model," International Journal of Forecasting, Elsevier, vol. 19(4), pages 603-622.
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    Cited by:

    1. Fidel Ernesto Castro Morales & Dimitris N. Politis & Jacek Leskow & Marina Silva Paez, 2022. "Student’s-t process with spatial deformation for spatio-temporal data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(5), pages 1099-1126, December.

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