Bayesian dynamic models for space–time point processes
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.
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- 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.
- 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.
- Håvard Rue & Sara Martino & Nicolas Chopin, 2009. "Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 319-392.
- Yosihiko Ogata, 1998. "Space-Time Point-Process Models for Earthquake Occurrences," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(2), pages 379-402, June.
- Anders Brix, 2001. "Space-time Multi Type Log Gaussian Cox Processes with a View to Modelling Weeds," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(3), pages 471-488.
- 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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