Causal Inference: Do-Operator & Back-Door Path
Structural Causal Model
U
confounder
X
Y
back-door path
Observational: P(Y | X=1)
Intervention: P(Y | do(X=1))
Show back-door path
Observational mode:
We observe units that happen to have X=1. Since U causes both X and Y, the observed group is biased (higher U → higher Y). The association is confounded.
Distribution of Y
P(Y | X=1) — associational (biased)
P(Y | do(X=1)) — interventional (true effect)