0386229 20240903170528.320130111235959.9 000312118700011 84879199459 10.1214/11-AIHP431 12 s. cav_un_epca*02507890246-0203484 (2012)1137-1147Institute of Mathematical Statistics Conditional independence Markov properties factorizable distributions graphical Markov models log-convexity Gibbs-Markov equivalence Markov fields Gaussian distributions positive definite matrices covariance selection model cav_un_auth*0101161 Matúš František Matematická teorie rozhodování Department of Decision Making Theory MTR MTR UTIA-B Department of Decision Making Theory Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2013/MTR/matus-0386229.pdf IAA100750603 GA AV ČR cav_un_auth*0216427 GA201/08/0539 GA ČR cav_un_auth*0239648 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. 2013 BA 4 A 4a 20231122135425.1 RVO:67985556 http://hdl.handle.net/11104/0216169 STATISTICSPROBABILITY 0.979 0.32 7.9 0.00536 1.254 623 50 24 1.926 29.36 0.97 Q1 67.887 50.855 Q2 Q1 2012 Soubory v repozitáři: matus-0386229.pdf 84879199459 SCOPUS 000312118700011 WOS cav_un_epca*0250789 Annales de L Institut Henri Poincare-Probabilites Et Statistiques 0246-0203 Roč. 48 č. 4 2012 1137 1147 Institute of Mathematical Statistics