Variable neighborhood random fields and neighborhood radius estimation
vendredi 7 janvier 2011, 14h30 - 15h30
Consider a Â random field on Z^d with finite spin space where the spin at eachÂ siteÂ depends on a « random » number of neighborhood symbols.Â This neighborhood is denotedÂ « context » of the site in analogy with the notion of variable-length Markov chains.
The aim is to findÂ a parsimonious description of the data by using higherÂ
order Markov dependencies whenÂ needed, and using lower order dependenciesÂ when possible.Â This is in the spirit of an extension to d -dimensions of the Minimum Description Length PrincipleÂ introduced by Rissanen 1983. WeÂ introduce an estimator of the length of the context.Â We prove the consistency of the estimator and give precise error bounds forÂ the probability of over- and underestimation. (work in collaboration with Eva LoecherbachÂ
ATTENTION CHANGEMENT DE SALLE:
Salle Fourier E au 4ème étage du bâtiment des Saints-Pères.