Institute of Information Theory and Automation

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Bibliography

Journal Article

On conditional independence and log-convexity

Matúš František

: Annales de L Institut Henri Poincare-Probabilites Et Statistiques vol.48, 4 (2012), p. 1137-1147

: IAA100750603, GA AV ČR, GA201/08/0539, GA ČR

: Conditional independence, Markov properties, factorizable distributions, graphical Markov models, log-convexity, Gibbs-Markov equivalence, Markov fields, Gaussian distributions, positive definite matrices, covariance selection model

: 10.1214/11-AIHP431

: http://library.utia.cas.cz/separaty/2013/MTR/matus-0386229.pdf

(eng): 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.

: BA

2019-01-07 08:39