I'm writing a research paper and considering the following settings:
There are three discrete variables which construct a simple causal graph: Treatment T, outcome Y, and confounders U. Here we have the classical causal path {T, U}->Y, U-> T.
We consider the following setting: We only have the marginal distribution of confounder P(U) and the joint distribution of observations P(X, Y). Then we're interested in some causal effect quantities, i.e., the interventional probability.
My question is: Could we show some realistic examples perfectly satisfying the above setting instead of some semi-synthetic examples? Some scenarios, like privacy protection, would be relevant.
I sincerely have no other idea and really appreciate your help!!~~I promise I will add your name warmly to the acknowledgement (even as a co-author).