The following is a synthetic proof in the normalization magmoid.
See also
- front-door adjustment formula, for the case where the confounding variable cannot be observed.
References
- Causality (Pearl, 2009)
- Compositional Inference for Bayesian Networks and Causality (Jacobs, Széles, Stein, 2025), argues this formula in the category of subdistributions using normalization boxes.
- https://math.stackexchange.com/questions/3544445/on-the-derivation-of-judea-pearls-front-door-adjustment-formula-in-the-book-of
- https://stats.stackexchange.com/questions/312992/causal-effect-by-back-door-and-front-door-adjustments/313127#313127
Tags: causality, normalization, NormStoch.