Pearl's attention to the do conditionality -- i.e., P(Y|do(X)) versus P(Y|X) is interesting and important in a certain sense, but I'm not sure it's really resolved debates about causality in any practical sense.
I don't really mean that in a dismissive sense, just to point out that his notation just begs the question of what do(X) means, in terms of why it is actually important. To me it just kind of formalizes a certain notation and kicks the hard theoretical can down the road.
In the books and papers I've read of Pearl's, he makes reasonable logical arguments for certain types of causal inferences, but when, in discussion with colleagues, we've tried to think of how they would be implemented outside the context of an experiment, we've been sort of at a loss. I say this as someone who identifies with observational study professionally, but who recognizes the importance of experiments.
My broader point is that I think Pearl's do-calculus can be reexpressed in traditional graph theory/structural equations/statistics without introducing anything new. In that sense, although I think his writings have drawn attention to important issues, I don't think they have solved anything.
> just to point out that his notation just begs the question of what do(X) means,
It's very formally specified. The key object of study in Pearl-style causal inference is a structural causal model. A structural causal model is composed as equations like the following:
Y = f(X, Z, U)
Here, X and Z are observed inputs, other random variables in your system. U is unobserved. In other words, "Y is computed by a deterministic function which takes an unknown random input."
Then, P(Y = 1 | do(X=1, Z=2)) is defined as P(f(1,2, U) = 1).
I don't really mean that in a dismissive sense, just to point out that his notation just begs the question of what do(X) means, in terms of why it is actually important. To me it just kind of formalizes a certain notation and kicks the hard theoretical can down the road.
In the books and papers I've read of Pearl's, he makes reasonable logical arguments for certain types of causal inferences, but when, in discussion with colleagues, we've tried to think of how they would be implemented outside the context of an experiment, we've been sort of at a loss. I say this as someone who identifies with observational study professionally, but who recognizes the importance of experiments.
My broader point is that I think Pearl's do-calculus can be reexpressed in traditional graph theory/structural equations/statistics without introducing anything new. In that sense, although I think his writings have drawn attention to important issues, I don't think they have solved anything.