On conditional independence and log-convexity

František Matúš

Annales de l'I.H.P. Probabilités et statistiques (2012)

  • Volume: 48, Issue: 4, page 1137-1147
  • ISSN: 0246-0203

Abstract

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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.

How to cite

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Matúš, František. "On conditional independence and log-convexity." Annales de l'I.H.P. Probabilités et statistiques 48.4 (2012): 1137-1147. <http://eudml.org/doc/271985>.

@article{Matúš2012,
abstract = {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.},
author = {Matúš, František},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {conditional independence; Markov properties; factorizable distributions; graphical Markov models; log-convexity; Gibbs–Markov equivalence; Markov fields; Hammersley–Clifford theorem; contingency tables; Gibbs potentials; multivariate gaussian distributions; positive definite matrices; covariance selection model; Gibbs-Markov equivalence; Hammersley-Clifford theorem; multivariate Gaussian distributions},
language = {eng},
number = {4},
pages = {1137-1147},
publisher = {Gauthier-Villars},
title = {On conditional independence and log-convexity},
url = {http://eudml.org/doc/271985},
volume = {48},
year = {2012},
}

TY - JOUR
AU - Matúš, František
TI - On conditional independence and log-convexity
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2012
PB - Gauthier-Villars
VL - 48
IS - 4
SP - 1137
EP - 1147
AB - 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.
LA - eng
KW - conditional independence; Markov properties; factorizable distributions; graphical Markov models; log-convexity; Gibbs–Markov equivalence; Markov fields; Hammersley–Clifford theorem; contingency tables; Gibbs potentials; multivariate gaussian distributions; positive definite matrices; covariance selection model; Gibbs-Markov equivalence; Hammersley-Clifford theorem; multivariate Gaussian distributions
UR - http://eudml.org/doc/271985
ER -

References

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