you're right that B is not a collider anymore since it's now conditioned on, but C is still a certified blocker.

again, in the intuitive example now we know your score and your math skills, easy test and good genes are independent of each other

]]>A is parent of B.

C is also parent of B.

D is parent of C.

The Markov blanket of A is B,C (child and parent of a child).

Means that A and D are independent give B,C. why? B is explaining away D.

What I'm missing?

Intuition: suppose C is "good grade". A and B are possible causes for the C, e.g. A = "easy test" and B = "math skill". D is a possible cause for B, e.g. D = "good genes".

If you know that someone got a good grade (C=1), then of course if the test was hard (A=0) then it makes it much more probable that he has good math skills (B=1), **and also** that he has good genes (D=1).

A very helpful guide for d-sep and explaining away is here: http://bayes.cs.ucla.edu/BOOK-2K/d-sep.html

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