Graphical Markov models use graphs, either undirected, directed, or mixed, to represent possible dependences among statistical variables. Applications of undirected graphs (UGs) include models forâ€¦ (More)

A multivariate Gaussian graphical Markov model for an undirected graph G, also called a covariance selection model or concentration graph model, is defined in terms of the Markov properties, i.e.,â€¦ (More)

Graphical Markov models use graphs ei ther undirected directed or mixed to rep resent possible dependences among statis tical variables Applications of undirected graphs UDGs include models forâ€¦ (More)

Bayesian networks, equivalently graphical Markov models determined by acyclic digraphs or ADGs (also called directed acyclic graphs or dags), have proved to be both effective and efficient forâ€¦ (More)

Acyclic digraphs (ADGs) are widely used to describe dependences among variables in multivariate distributions. In particular, the likelihood functions of ADG models admit convenient recursiveâ€¦ (More)

Pearlâ€™s well-known d-separation criterion for an acylic directed graph (ADG) is a pathwise separation criterion that can be used to efficiently identify all valid conditional independence relationsâ€¦ (More)

Indiana University and the University of Washington 2Chain graphs (CG) (= adicyclic graphs) use undirected and directed edges to represent simultaneously both structural and associative dependences..â€¦ (More)

Multivariate Gaussian graphical models are defined in terms of Markov properties, i.e., conditional independences associated with the underlying graph. Thus, model selection can be performed byâ€¦ (More)

A multivariate normal statistical model defined by the Markov properties determined by an acyclic digraph admits a recursive factorization of its likelihood function (LF) into the product ofâ€¦ (More)