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  • 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.
  • 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. (en)
Title
  • On conditional independence and log-convexity
  • On conditional independence and log-convexity (en)
skos:prefLabel
  • On conditional independence and log-convexity
  • On conditional independence and log-convexity (en)
skos:notation
  • RIV/67985556:_____/12:00386229!RIV13-AV0-67985556
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  • Conditional independence; Markov properties; factorizable distributions; graphical Markov models; log-convexity; Gibbs-Markov equivalence; Markov fields; Gaussian distributions; positive definite matrices; covariance selection model (en)
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  • Annales de L Institut Henri Poincare-Probabilites Et Statistiques
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  • 48
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  • Matúš, František
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  • 000312118700011
issn
  • 0246-0203
number of pages
http://bibframe.org/vocab/doi
  • 10.1214/11-AIHP431
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