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Spatio-Temporal Model for a Random Set Given by a Union of Interacting Discs

Author

Listed:
  • Markéta Zikmundová

    (Charles University in Prague)

  • Kateřina Staňková Helisová

    (Czech Technical University in Prague)

  • Viktor Beneš

    (Charles University in Prague)

Abstract

A spatio-temporal random set parametric model is defined based on the union of interacting discs. There are two types of parameters: those of the spatial part of the model and those of the state space model for temporal evolution. The simulation of the random set is available using a Markov chain Monte Carlo algorithm. Integral-geometric characteristics are evaluated and serve as an input to parameter estimation. We compare an MCMC maximum likelihood estimator with a particle filter estimator in a simulation study by drawing their temporal evolution and globally by means of the integrated mean square error. Interpretations of parameters and possible applications are discussed.

Suggested Citation

  • Markéta Zikmundová & Kateřina Staňková Helisová & Viktor Beneš, 2012. "Spatio-Temporal Model for a Random Set Given by a Union of Interacting Discs," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 883-894, September.
    • Handle: RePEc:spr:metcap:v:14:y:2012:i:3:d:10.1007_s11009-012-9287-6
    DOI: 10.1007/s11009-012-9287-6
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    References listed on IDEAS

    as
    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.
    2. Jesper Møller & Kateřina Helisová, 2010. "Likelihood Inference for Unions of Interacting Discs," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(3), pages 365-381, September.
    3. 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.
    4. Anders Brix & Jesper Moller, 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, September.
    5. Roger D. Peng & Frederic Paik Schoenberg & James A. Woods, 2005. "A Space-Time Conditional Intensity Model for Evaluating a Wildfire Hazard Index," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 26-35, March.
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    Cited by:

    1. Kateřina Staňková Helisová & Jakub Staněk, 2014. "Dimension Reduction in Extended Quermass-Interaction Process," Methodology and Computing in Applied Probability, Springer, vol. 16(2), pages 355-368, June.
    2. Markéta Zikmundová & Kateřina Staňková Helisová & Viktor Beneš, 2014. "On the Use of Particle Markov Chain Monte Carlo in Parameter Estimation of Space-Time Interacting Discs," Methodology and Computing in Applied Probability, Springer, vol. 16(2), pages 451-463, June.

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