Question to author:
I am writing a precis of this book.
In the do-calculus inference rules, I understand how the subgraph is generated from the submodel do(X = x), Gx, the removal of direct causes and therefore d-separation is a valid test for conditional independence. However I don't understand the submodel for subgraphs representing the removal of direct effects. Would you please explain the submodel I could use to explain this subgraph and what distribution it represents.
The removal of direct effects leaves us with a graph in which X cannot effect Y, so if X and Y are not d-separated in that graph it must be due to (unblocked) confounding paths between the two. Therefore, if we condition on a set Z of variables that blocks all such paths we are assured that we have neutralized all confounders and whatever dependence we measure after such conditioning must be due to the causal effect of X on Y, free of confoundings. This gives us the license to equate measured dependence with the causal effect.
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