Maximisation for graphs
Max generates a maximal graph that induces the same
independence model from a non-maximal graph.
An adjacency matrix, or a graph that can be a
Max looks for non-adjacent pais of nodes that are connected by
primitive inducing paths, and connect such pairs by an appropriate edge.
A matrix that consists 4 different integers as an ij-element: 0 for a missing edge between i and j, 1 for an arrow from i to j, 10 for a full line between i and j, and 100 for a bi-directed arrow between i and j. These numbers are added to be associated with multiple edges of different types. The matrix is symmetric w.r.t full lines and bi-directed arrows.
Richardson, T.S. and Spirtes, P. (2002). Ancestral graph Markov models. Annals of Statistics, 30(4), 962-1030.
Sadeghi, K. and Lauritzen, S.L. (2011). Markov properties for loopless mixed graphs. Submitted. http://arxiv.org/abs/1109.5909.
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