Comments on: d-Separation Without Tears
https://causality.cs.ucla.edu/blog/index.php/2000/01/01/d-separation-without-tears/
UCLA Causality BlogFri, 19 Sep 2014 01:02:03 +0000
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By: Zane
https://causality.cs.ucla.edu/blog/index.php/2000/01/01/d-separation-without-tears/#comment-4
Fri, 19 Sep 2014 01:02:03 +0000http://www.mii.ucla.edu/causality/?p=15#comment-4Typo: collider-tree -> collider-free
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By: Guillaume
https://causality.cs.ucla.edu/blog/index.php/2000/01/01/d-separation-without-tears/#comment-3
Wed, 12 Aug 2009 14:34:38 +0000http://www.mii.ucla.edu/causality/?p=15#comment-3I have a technical question regarding d-separation (dsep). In Pearl's 1988 book, Theorem 12 (p 129) states that dsep is wealy transitive. Proving this result is performed by showing that the contrapose of (3.34f) holds. However, while the conditioning set (Z) is central in the definition of weak transitivity (it has to be the same), no such mention is found in the proof. As a matter of fact, what is shown is that, if we have not-I(X,Z1,gamma) and not-I(gamma, Z2,Y), then we also have either not-I(X,Z1 u Z2,Y) or not-I(X,Z1 u Z2 u gamma,Y). Does it mean that the definition of weak transitivity is incorrect and should be changed, or that in the proof we must only consider sets for which Z1 = Z2? Wouldn't this second option reduce the interest of the result and hint the definition of an "extended" weak transitivity?
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