Partially Observed Markov Random Fields Are Variable Neighborhood Random Fields
| Autor: | Antonio Galves, Eva Löcherbach, Marzio Cassandro |
|---|---|
| Rok vydání: | 2012 |
| Předmět: |
Phase transition
Random field Markov random field Markov chain Probability (math.PR) 010102 general mathematics Statistical and Nonlinear Physics 01 natural sciences k-nearest neighbors algorithm 010104 statistics & probability FOS: Mathematics 60G60 60K35 (Primary) 82B20 82B99 (Secondary) Almost surely Ising model Statistical physics 0101 mathematics Mathematics - Probability Mathematical Physics Mathematics Variable (mathematics) |
| Zdroj: | Journal of Statistical Physics. 147:795-807 |
| ISSN: | 1572-9613 0022-4715 |
| DOI: | 10.1007/s10955-012-0488-8 |
| Popis: | The present paper has two goals. First to present a natural example of a new class of random fields which are the variable neighborhood random fields. The example we consider is a partially observed nearest neighbor binary Markov random field. The second goal is to establish sufficient conditions ensuring that the variable neighborhoods are almost surely finite. We discuss the relationship between the almost sure finiteness of the interaction neighborhoods and the presence/absence of phase transition of the underlying Markov random field. In the case where the underlying random field has no phase transition we show that the finiteness of neighborhoods depends on a specific relation between the noise level and the minimum values of the one-point specification of the Markov random field. The case in which there is phase transition is addressed in the frame of the ferromagnetic Ising model. We prove that the existence of infinite interaction neighborhoods depends on the phase. To appear in Journal of Statistical Physics |
| Databáze: | OpenAIRE |
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