Enza Orlandi (Università di Roma TRE)

Variable neighborhood random fields and neighborhood radius estimation

vendredi 7 janvier 2011, 14h30 - 15h30

Salle de réunion, espace Turing

Consider a  random field on Z^d with finite spin space where the spin at each site depends on a « random » number of neighborhood symbols. This neighborhood is denoted « context » of the site in analogy with the notion of variable-length Markov chains.

The aim is to find a parsimonious description of the data by using higher 
order Markov dependencies when needed, and using lower order dependencies when possible.  This is in the spirit of an extension to d -dimensions of the Minimum Description Length Principle introduced by Rissanen 1983. We introduce an estimator of the length of the context. We prove the consistency of the estimator and give precise error bounds for the probability of over- and underestimation. (work in collaboration with Eva Loecherbach 

Salle Fourier E au 4ème étage du bâtiment des Saints-Pères.