Publication at Faculty of Mathematics and Physics |
2012
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.