t-separation and d-separation for Directed Acyclic Graphs

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In recent work, Sullivant and Talaska [2008] introduced a new separation criterion, t-separation, for DAGs. They showed that for a Gaussian DAG model, t-separation characterizes when a submatrix of the variance-covariance matrix will have non-full rank. In particular, special forms of t-separation characterize all conditional independence statements for the Gaussian DAG model. This indirectly proved that these special forms of t-separation are equivalent to the d-separation criterion, since d-separation also characterizes all conditional independence statements for a Gaussian DAG model. In this report, we present a direct graph-theoretic proof of the equivalence between the special forms of t-separation and d-separation


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