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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\{s, t}, 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.

Drton, Mathias and Thomas Richardson. Iterative Conditional Fitting for Gaussian Ancestral Graph Models. Technical Report 437, December 2003.

See also


Graduate Texts in Mathematics

Graduate Studies in Mathematics

Mathematics Encyclopedia



Hellenica World - Scientific Library

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