2014/12/02 by Hélène Massam, Massam, Helene, Jacek Wesołowski +1
Computer Science · Mathematics · #62E99 #62F15 #62H17 #Bayesian Methods and Mixture Models #Bayesian Modeling and Causal Inference #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1412.0972
openalex publication_date 2014/12/02 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
In this paper, we first develop a new family of conjugate prior distributions\nfor the cell parameters of discrete graphical models Markov with respect to a\nset P of moral directed acyclic graphs with skeleton a given decomposable graph\nG. Such families arise when the set of conditional independences between\ndiscrete variables is given and can be represented by a decomposable graph and\nadditionally, the direction of certain edges is imposed by the practitioner.\nThis family, which we call the P-Dirichlet, is a generalization of the hyper\nDirichlet given in Dawid and Lauritzen (1993): it keeps the strong directed\nhyper Markov property for every DAG in P but increases the flexibility in the\nchoice of its parameters, i.e. the hyper parameters. Our second contribution is\na characterization of the P-Dirichlet, which yields, as a corollary, a\ncharacterization of the hyper Dirichlet and a characterization of the Dirichlet\nalso. Like that given by Geiger and Heckerman (1997), our characterization of\nthe Dirichlet is based on local and global independence of the probability\nparameters but we need not make the assumption of the existence of a positive\ndensity function. We use the method of moments for our proofs.\n