MMP.15:4.2 - Recover the available laws and the admissible causal models

Use MMP.7 to recover how records arise. With inclusion indicator (S), selected records supply a law such as (P(A,Y,L\mid S=1)), not automatically (P(A,Y,L)). Keep assignment, actual action, measurement and inclusion distinct when those distinctions affect the target. State which variables were jointly observed, which interventions were performed, and which population each source concerns.

For identification, provisionally treat these population laws as known. This asks what unlimited data of those kinds could determine. MMP.13 handles finite-sample estimation.

Describe the admitted causal relations. An acyclic causal graph is a useful representation: directed arrows allow direct causal influence, and a shared unobserved cause can be represented explicitly or by a bidirected edge. The absence of an arrow excludes a possible influence relative to the represented variables. A good observational fit does not justify that exclusion. Time-indexed variables can express feedback across time; a theorem for acyclic graphs must not be applied unchanged to an equilibrium model with unresolved cycles.

When these causal relations or material rival mechanisms still need construction, C.28.CM develops the model family, its subject meanings and the consequences that could distinguish its members. Bring that result back to the identification question. A sufficient already supplied family needs no additional construction.

The operative identification test is this: whenever two admitted causal models induce the same available laws, must they give the same requested quantity? If the assumptions themselves conflict with the available laws, return that conflict rather than declaring a result identified through an empty model class.