Parameter Estimation for Gibbs Distributions from Partially Observed Data
Comets, Francis ; Gidas, Basilis
Ann. Appl. Probab., Tome 2 (1992) no. 4, p. 142-170 / Harvested from Project Euclid
We study parameter estimation for Markov random fields (MRFs) over $Z^d, d \geq 1$, from incomplete (degraded) data. The MRFs are parameterized by points in a set $\Theta \subseteq \mathbb{R}^m, m \geq 1$. The interactions are translation invariant but not necessarily of finite range, and the single-pixel random variables take values in a compact space. The observed (degraded) process $y$ takes values in a Polish space, and it is related to the unobserved MRF $x$ via a conditional probability $P^{y \mid x}$. Under natural assumptions on $P^{y \mid x}$, we show that the ML estimations are strongly consistent irrespective of phase transitions, ergodicity or stationarity, provided that $\Theta$ is compact. The same result holds for noncompact $\Theta$ under an extra assumption on the pressure of the MRFs.
Publié le : 1992-02-14
Classification:  Gibbs fields,  large deviations,  maximum likelihood,  variational principle,  60F10,  62F99
@article{1177005775,
     author = {Comets, Francis and Gidas, Basilis},
     title = {Parameter Estimation for Gibbs Distributions from Partially Observed Data},
     journal = {Ann. Appl. Probab.},
     volume = {2},
     number = {4},
     year = {1992},
     pages = { 142-170},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177005775}
}
Comets, Francis; Gidas, Basilis. Parameter Estimation for Gibbs Distributions from Partially Observed Data. Ann. Appl. Probab., Tome 2 (1992) no. 4, pp.  142-170. http://gdmltest.u-ga.fr/item/1177005775/