Probabilistic graphical model

A probabilistic graphical model represents factorization and conditional-independence structure using a graph whose vertices are random variables.

A Markov random field is an undirected graphical model whose graph encodes conditional independence by vertex separation.

A clique potential is a nonnegative function of the variables belonging to one clique. Products of clique potentials define the unnormalized density of a Markov random field.

The global Markov property says that graph separation of vertex sets $A$ and $B$ by $S$ implies conditional independence of the corresponding random vectors given the variables at $S$.