Causal Inference — do-Calculus & Backdoor Criterion

Pearl's do-calculus distinguishes P(Y|X) (observation) from P(Y|do(X)) (intervention). The backdoor criterion identifies confounding paths that must be blocked.

True causal effect α0.80

Confounder strength γ1.20

Sample size N300

Noise σ0.50

DAG: Z (confounder) → X (treatment) and Z → Y (outcome). Backdoor path: X ← Z → Y. Conditioning on Z blocks this path, recovering P(Y|do(X)) = Σ_z P(Y|X,Z=z)P(Z=z).