Control confounding in observational ad lift

Ad exposure cannot be randomized. Users vary by age, education, and income. Propose a causal inference plan for estimating the ATE of ad exposure on conversions. Include: (1) a DAG that supports a valid adjustment set; (2) a propensity score model, plus either matching or inverse-probability weighting with stabilized weights; (3) the ATE formulas for IPW and doubly robust (AIPW) estimators; (4) diagnostics (overlap checks, standardized mean differences before and after, effective sample size, weight trimming); (5) sensitivity analysis for unobserved confounding (e.g., Rosenbaum bounds); (6) avoiding post-treatment bias (excluding engagement mediators); (7) variance estimation and how to report uncertainty. Discuss when you would prefer diff-in-diff or CUPED, and the required assumptions. Overview: This question assesses mastery of observational causal inference for ATE estimation, including causal DAGs and identification, pre-treatment adjustment, propensity-score and inverse-probability/doubly-robust estimation, diagnostic checks, sensitivity analysis for unobserved confounding, and variance/uncertainty quantification in ad exposure data. It is frequently asked because real-world advertising analyses cannot rely on randomization, and interviewers need confidence in both conceptual understanding of identification assumptions and practical application of estimation and diagnostic techniques; the category is Statistics & Math, and the level of abstraction spans conceptual reasoning and applied implementation.