Rubin Potential Outcomes & DAG d-Separation

The Dual Foundations of Causal Inference (Donald Rubin's Potential Outcomes Framework & Judea Pearl's Causal DAGs / $d$-Separation) provides mathematical identification of causal treatment effects from purely observational data when randomized A/B tests are impossible; Fundamental Problem of Causal Inference: for unit $i$, only one factual potential outcome $Y_i(1)$ or $Y_i(0)$ is observable while the other remains an unobservable counterfactual; Average Treatment Effect $\text{ATE} = \mathbb{E}[Y(1) - Y(0)]$; Pearl's 3 Causal Graph Junctions: 1) Chain ($A \to B \to C$); 2) Fork ($A \leftarrow Z \to B$, $Z$ is a confounder generating spurious correlation, requiring conditioning on $Z$ via Backdoor Criterion); 3) Collider ($A \to C \leftarrow B$, $C$ is a collider; conditioning on $C$ must be avoided as it unblocks spurious paths and induces Berkson's Paradox); $d$-Separation establishes graph-theoretic necessity for confounder adjustment.

Observational causal policy evaluation, identifying confounders, and rigorous backdoor adjustment proofs.

Observational correlation masks true causality; DAGs and $d$-separation prevent collider bias and confounding from distorting empirical business conclusions.

Derive Pearl's Backdoor and Frontdoor criteria with graph-theoretic $d$-separation blocking conditions?

Diagram Collider Bias (Berkson's Fallacy) and illustrate how conditioning on a collider creates spurious negative correlations?

Explain the 3 foundational assumptions of Potential Outcomes: Ignorability, Positivity/Overlap, and SUTVA in practice?

Why does conditioning on post-treatment mediators in regression models attenuate and bias the total causal treatment effect?

Contrast Pearl's causal intervention distribution $P(Y | do(X=x))$ with the observational conditional distribution $P(Y | X=x)$ using do-calculus?