On conditional independence and log-convexity. (English. French summary) Zbl 1253.62036

Summary: If conditional independence constraints define a family of positive distributions that is log-convex then this family turns out to be a Markov model over an undirected graph. This is proved for the distributions on products of finite sets and for the regular Gaussian ones. As a consequence, the assertion known as Brook factorization theorem, Hammersley-Clifford theorem or Gibbs-Markov equivalence is obtained.


62H05 Characterization and structure theory for multivariate probability distributions; copulas
62M40 Random fields; image analysis
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
62H17 Contingency tables
62J10 Analysis of variance and covariance (ANOVA)
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