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

Markéta Zikmundová, Kateřina Staňková Helisová () and Viktor Beneš ()
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Markéta Zikmundová: Charles University in Prague
Kateřina Staňková Helisová: Czech Technical University in Prague
Viktor Beneš: Charles University in Prague

Methodology and Computing in Applied Probability, 2012, vol. 14, issue 3, 883-894

Abstract: 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.

Keywords: Germ-grain model; Particle filter; Spatio-temporal random set; 60D05; 60G55 (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11009-012-9287-6

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