[For the entire collection see Zbl 0718.68001.]
The main contributions of the paper are: (1) To develop an efficient algorithm for detecting the conditional independencies directly from the topology of the network, by merely examining the connection paths. The proposed algorithm is based on a graphical criterion, called ḏ- separation, that associates the topology of the network to independencies encoded in the underlying distribution. The main property of ḏ- separation is that it detects only genuine independencies of the underlying distribution, and it can not be sharpened to reveal additional independencies. The soundness and completeness of ḏ-separation with respect to probability theory have as consequences the correctness and maximality of the algorithm. It runs in polynomial time depending on the number of edges in the network. (2) The second important contribution of the paper is to provide a unified approach to the solution of two distinct problems: sensitivity to parameter values, and sensitivity to variable instantiations.