ⓘ M-separation. In statistics, m -separation is a measure of disconnectedness in ancestral graphs and a generalization of d-separation for directed acyclic graphs ..


ⓘ 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.

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