information:extraction
Definition

In principle, the defining equality P (y ∣ do (x)) = P (y ∣ x) {\displaystyle P(y\mid {\text{do}}(x))=P(y\mid x)} can be verified from the data generating model, assuming we have all the equations and probabilities associated with the model. This is done by simulating an intervention do (X = x) {\displaystyle {\text{do}}(X=x)} (see Bayesian network) and checking whether the resulting probability of Y equals the conditional probability P (y ∣ x) {\displaystyle P(y\mid x)}. It turns out, however, that graph structure alone is sufficient for verifying the equality P (y ∣ do (x)) = P (y ∣ x) {\displaystyle P(y\mid {\text{do}}(x))=P(y\mid x)}.