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# Markov Random Fields

A family of random variables  is said to be a Markov Random Field on S with respect to a neighborhood system if and only if:

being the neighborhood system.

Neighborhood system for a Markov Random Field of order1 and corresponding cliques with cardinal lower or equal to 2:

Hammersley-Clifford theorem: A Markov Random Field can be written as a Gibbs distribution,

Christine Hivernat & Xavier Descombes

November 1998