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Common terms and phrasesalgorithm asymptotic bases binary random variables binomials chain graph chi-square coefficient compute conditional independence conditional independence constraints conditional independence ideal conditional independence model conditional independence statements consider correspond covariance matrix d-separates defined denote density diagonal different discrete random variables entries equal Example exponential family fiber finite first fixed Fm,s global Markov property Gr¨obner basis graph G hidden variables intersection axiom lattice likelihood equations likelihood function likelihood ratio statistic linear log-likelihood function log-linear model marginal likelihood Markov property maximum likelihood estimates minimal Markov basis Mixt2(M mixture model ML degree model associated monomial multivariate normal distribution nodes non-negative non-zero p-value pairwise parameter space polynomial positive definite probability distributions probability simplex problem Proof Proposition random vector rank sample satisfies secant variety Section semi-algebraic set simplicial complex Singular solutions statistical models subset sufficient statistics tangent cone Theorem undirected graph undirected graphical models Zariski closure zero Bibliographic information
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