Given the following casual graph, we need to find the formula for $P(y|do(a))$ in terms of observed variables Y, A, W, M.
My attempt is to try different back-door and front-door adjustment sets, however, I don't see any. Most likely, I need to use Pearl’s do calculus but how can I do it?
How to solve it with Pearl’s do calculus?
An answer using do-calculus would be quite tedious, which is why most causal inference packages such as do-why abstract away from it. Since you seem to care about adjustment sets you can use graphical criteria (blocking all open backdoor paths), to see that you'd have to condition on $U_2$. The software daggity (and many others) has some nice tools to do perform this step automatically.
