We consider random fields defined by finite-region conditional probabilities depending on a neighborhood of the region which changes with the boundary conditions. To predict the symbols within any finite region, it is necessary to inspect a random number of neighborhood symbols which might change according to the value of them. In analogy with the one-dimensional setting we call these neighborhood symbols the context associated to the region at hand. This framework is a natural extension, to d dimensional fields, of the notion of variable length Markov chains introduced by Rissanen [26] in his classical paper. We define an algorithm to estimate the radius of the smallest ball containing the context based on a realization of the field. We prove the consistency of this estimator. Our proofs are constructive and yield explicit upper bounds for the probability of wrong estimation of the radius of the context.

Locherbach, E., Orlandi, V. (2011). Neighborhood radius estimation in Variable-neighborhood Random Fields. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 121, 2151-2185 [10.1016/j.spa.2011.05.001].

Neighborhood radius estimation in Variable-neighborhood Random Fields

ORLANDI, Vincenza
2011-01-01

Abstract

We consider random fields defined by finite-region conditional probabilities depending on a neighborhood of the region which changes with the boundary conditions. To predict the symbols within any finite region, it is necessary to inspect a random number of neighborhood symbols which might change according to the value of them. In analogy with the one-dimensional setting we call these neighborhood symbols the context associated to the region at hand. This framework is a natural extension, to d dimensional fields, of the notion of variable length Markov chains introduced by Rissanen [26] in his classical paper. We define an algorithm to estimate the radius of the smallest ball containing the context based on a realization of the field. We prove the consistency of this estimator. Our proofs are constructive and yield explicit upper bounds for the probability of wrong estimation of the radius of the context.
2011
Locherbach, E., Orlandi, V. (2011). Neighborhood radius estimation in Variable-neighborhood Random Fields. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 121, 2151-2185 [10.1016/j.spa.2011.05.001].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/123046
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