Let us consider variables $A,B,C,D$ such that

  • $A$ is conditionally independent of $B$ given $C$, i.e. $A \bot B|C$
  • $A$ is conditionally dependent on $B$ given $D$, i.e. $A \not\bot B|D$

Are $A$ and $B$ conditionally independent of each other given $C,D$? Are they not? Can we conclude anything about their conditional independence?

That is, can we say anything about the following claim? $A \bot B|C,D$


1 Answer 1


A situation where $A \perp B \mid C, D$ (dependence arrows run top-to-bottom, i.e. $C \to A$):

D       C
      /   \
     A     B

A situation where $A \not\perp B \mid C, D$:

 / \
A   B
 \ /

So we can't say one way or the other.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.