Lesson plan
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.
Article summary
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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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
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Key claims and bibliography are generated from the same tracked claims and sources as the article page.