Editing Markov random field (section)

== Examples ==

=== Gaussian ===
A [[multivariate normal distribution]] forms a Markov random field with respect to a graph <math>G=(V,E)</math> if the missing edges correspond to zeros on the [[precision matrix]] (the inverse [[covariance matrix]]):

:<math>X=(X_v)_{v\in V} \sim \mathcal N (\boldsymbol \mu, \Sigma)
</math>
such that
:<math>(\Sigma^{-1})_{uv} =0 \quad \text{iff} \quad \{u,v\} \notin E .</math><ref>{{cite book
 |first1=Håvard |last1=Rue |first2=Leonhard |last2=Held
 |title=Gaussian Markov random fields: theory and applications
 |publisher=CRC Press |year=2005
 |isbn=978-1-58488-432-3
}}</ref>