M-separation

M-separation

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.

References

*Drton, Mathias and Thomas Richardson. "Iterative Conditional Fitting for Gaussian Ancestral Graph Models". [http://www.stat.washington.edu/www/research/reports/2003/tr437.pdf Technical Report 437] , December 2003.

ee also

* d-separation


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