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Markov chain Markov field dynamics: models and statistics
Guyon, Xavier ; Hardouin, Cécile
HAL, hal-00110370 / Harvested from HAL
Text on HAL
This study deals with time dynamics of Markov fields defined on a finite set of sites with state space $E$, focussing on Markov chain Markov field (MCMF) evolution. Such a model is characterized by two families of potentials: the instantaneous interaction potentials and the time-delay potentials. Four models are specified: auto-exponential dynamics $(E=\Bbb R^+)$, auto-normal dynamics $(E=\Bbb R)$, auto-Poissonian dynamics $(E=\Bbb N)$ and autologistic dynamics ($E$ qualitative and finite). Sufficient conditions ensuring ergodicity and strong law of large numbers are given by using a Lyapunov criterion of stability, and the conditional pseudo-likelihood statistics are summarized. We discuss the identification procedure of the two Markovian graphs and look for validation tests using martingale central limit theorems. An application to meteorological data illustrates such a modelling.
Publié le : 2002-07-05
Classification:  Markov Field,  Markov Chain Dynamics,  Auto-model,  Lyapunov Stability Criterion,  Martingale Clt Theorem,  Model Diagnostic,  60J05 (62E20 62M05),  [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST],  [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH] 
@article{hal-00110370,
     author = {Guyon, Xavier and Hardouin, C\'ecile},
     title = {Markov chain Markov field dynamics: models and statistics},
     journal = {HAL},
     volume = {2002},
     number = {0},
     year = {2002},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00110370}
}

Guyon, Xavier; Hardouin, Cécile. Markov chain Markov field dynamics: models and statistics. HAL, Tome 2002 (2002) no. 0, . http://gdmltest.u-ga.fr/item/hal-00110370/