Glossary Entry

Do-Operator

Pearl's notation do(T = t) for setting a variable by intervention rather than observing it, separating P(Y given do(T)) from the ordinary conditional P(Y given T).

Statistics Decision Making

Also called: do-calculus, do operator

Seed source: Causality (Pearl, 2009)

Conditioning filters the data we look at; intervening changes the system that generates it. The do-operator marks the difference: P(Y

T = 1) describes customers who happened to be treated, while P(Y

do(T = 1)) describes the world where we force treatment on everyone. The two coincide only under identification assumptions, and the gap between them is exactly the bias in naive comparisons.

Do-calculus is the set of three rewrite rules for converting do-expressions into ordinary observational probabilities when the causal graph permits, with the backdoor and front-door adjustment formulas as its most used special cases. It is complete: if an effect is identifiable from a graph at all, the rules can derive the formula.