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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*