Definition Structural Causal Model [efr-0003]

Let G be a (finite) directed acyclic graph (DAG). Then a structural causal model (SCM) on G consists of

  • For each vertex v \in V(G), measurable spaces \mathcal {X}_v, \mathcal {E}_v
  • A family of independent random variables E_v \in \mathcal {E}_v---these are called the exogenous variables
  • For each v, a measurable function \phi _v: \mathcal {E}_v \times \prod _{v' \to v} \mathcal {X}_{v'} \to \mathcal {X}_v (note that if v has no parents, the product is just a singleton)