# Independence imply d-separation?

In the context of Bayesian networks if two random variables (i.e. nodes) are d-separated, they are independent. However, is there any example of random variables being independent but not d-separated?

The Yes answer: The comment by usεr11852 touches on the issue of faithfulness: there may be a zero measure of average causal effect (ACE), even if the sharp causal null hypothesis is false. For example, if (1) $$A$$ causes $$Y$$ (both dichotomous) because for some individuals $$Y^{a=1}\ne Y^{a=0}$$, but in some individuals $$Y^{a=1} - Y^{a=0} = 1$$ and in others $$Y^{a=1} - Y^{a=0} = -1$$ and (2) the number of individuals in each group is the same, then although there are individual causal effects, the ACE is zero, and the measure of association is unfaithful because $$A$$ & $$Y$$ are not d-separated.