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In statistics, ''m''-separation is a measure of disconnectedness in ancestral graphs and a generalization of d-separation for directed acyclic graphs. It is the opposite of ''m''-connectedness. Suppose ''G'' is an ancestral graph. For given source and target nodes ''s'' and ''t'' and a set ''Z'' of nodes in ''G''\, m-connectedness can be defined as follows. Consider a path from ''s'' to ''t''. An intermediate node on the path is called a ''collider'' if both edges on the path touching it are directed toward the node. The path is said to ''m-connect'' the nodes ''s'' and ''t'', given ''Z'', if and only if: *every non-collider on the path is outside ''Z'', and *for each collider ''c'' on the path, either ''c'' is in ''Z'' or there is a directed path from ''c'' to an element of ''Z''. If ''s'' and ''t'' cannot be ''m''-connected by any path satisfying the above conditions, then the nodes are said to be ''m-separated''. The definition can be extended to node sets ''S'' and ''T''. Specifically, ''S'' and ''T'' are ''m''-connected if each node in ''S'' can be ''m''-connected to any node in ''T'', and are ''m''-separated otherwise. ==References== *Drton, Mathias and Thomas Richardson. ''Iterative Conditional Fitting for Gaussian Ancestral Graph Models''. (Technical Report 437 ), December 2003. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「M-separation」の詳細全文を読む スポンサード リンク
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