Causal Graph

A causal graph (or causal DAG — directed acyclic graph) is a graphical model in which nodes represent variables and directed edges represent direct causal relationships between them. Developed formally by Judea Pearl and Sewall Wright (earlier, as path analysis), causal graphs provide a mathematical language for representing causal structure, distinguishing observational and interventional questions, and identifying which statistical estimates can recover causal effects from observational data. The key operation is do-calculus: Pearl's formalism allows the question "what is the probability of Y given that we intervene to set X = x?" (written P(Y | do(X = x))) to be distinguished from "what is the probability of Y given we observe X = x?" (written P(Y | X = x)). The two are different whenever there are confounders — common causes of X and Y. A randomized controlled trial implements do(X = x) by design; observational studies must use causal graphs and additional assumptions to approximate it. Causal graphs also clarify when adjustment for observed confounders is sufficient for identification — the back-door and front-door criteria — and when it is not. The framework has unified statistical causal inference, econometric identification, epidemiological study design, and parts of machine learning under a single conceptual structure.