From: Susan Scott, Australia

Subject: Causality (2000)

**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.

**Author's reply:**

Dear Susan,

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.

Next discussion (Hoyer: *The meaning of
counterfactuals *)