## Strong Markov Random Field Model

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### BibTeX

@MISC{Paget_strongmarkov,

author = {Rupert Paget},

title = {Strong Markov Random Field Model},

year = {}

}

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### Abstract

The strong Markov random field (MRF) model is a sub-model of the more general MRF-Gibbs model. The strong-MRF model defines a system whereby not only is the field Markovian with respect to a defined neighbourhood, but all sub-neighbourhoods also define a Markovian system. A checkerboard pattern is a perfect example of a strong Markovian system. Although the strong Markovian system requires a more stringent assumption about the field, it does have some very nice mathematical properties. One mathematical property, is the ability to define the strong Markov random field model with respect to its marginal distributions over the cliques. This property allows a direct equivalence to the ANOVA loglinear construction to be proved. From this proof, the general ANOVA log-linear construction formula is derived.