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Hierarchical Bayesian modeling of marked non-homogeneous Poisson processes with finite mixtures and inclusion of covariate information

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  • Athanasios Christou Micheas

Abstract

We investigate marked non-homogeneous Poisson processes using finite mixtures of bivariate normal components to model the spatial intensity function. We employ a Bayesian hierarchical framework for estimation of the parameters in the model, and propose an approach for including covariate information in this context. The methodology is exemplified through an application involving modeling of and inference for tornado occurrences.

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  • Athanasios Christou Micheas, 2014. "Hierarchical Bayesian modeling of marked non-homogeneous Poisson processes with finite mixtures and inclusion of covariate information," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(12), pages 2596-2615, December.
    • Handle: RePEc:taf:japsta:v:41:y:2014:i:12:p:2596-2615
    DOI: 10.1080/02664763.2014.922167
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    References listed on IDEAS

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    1. Stephen L. Rathbun & Saul Shiffman & Chad J. Gwaltney, 2007. "Modelling the effects of partially observed covariates on Poisson process intensity," Biometrika, Biometrika Trust, vol. 94(1), pages 153-165.
    2. Olivier Cappé & Christian P. Robert & Tobias Rydén, 2003. "Reversible jump, birth‐and‐death and more general continuous time Markov chain Monte Carlo samplers," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(3), pages 679-700, August.
    3. Sylvia. Richardson & Peter J. Green, 1997. "On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(4), pages 731-792.
    4. 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, April.
    5. repec:dau:papers:123456789/6040 is not listed on IDEAS
    6. Finn Lindgren & Håvard Rue & Johan Lindström, 2011. "An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(4), pages 423-498, September.
    7. Jesper Møller & Rasmus P. Waagepetersen, 2007. "Modern Statistics for Spatial Point Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(4), pages 643-684, December.
    8. Hossain, Md. Monir & Lawson, Andrew B., 2009. "Approximate methods in Bayesian point process spatial models," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 2831-2842, June.
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    Cited by:

    1. Zhengyi Zhou & David S. Matteson & Dawn B. Woodard & Shane G. Henderson & Athanasios C. Micheas, 2015. "A Spatio-Temporal Point Process Model for Ambulance Demand," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 6-15, March.
    2. G. Avlogiaris & A. C. Micheas & K. Zografos, 2019. "A Criterion for Local Model Selection," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(2), pages 406-444, December.
    3. Athanasios C. Micheas & Jiaxun Chen, 2018. "sppmix: Poisson point process modeling using normal mixture models," Computational Statistics, Springer, vol. 33(4), pages 1767-1798, December.

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