C.28:4.4 - Identification result

Identification answers whether the estimand can be expressed or bounded from the available data and assumptions. The bounds for nonidentified counterfactual queries in Raghavan and Bareinboim, 2026, §5 belong to this identification problem. The conclusion must be replayable:

CausalIdentificationResult:
  causalUseQuestionRef: CausalUseQuestionRef
  causalEstimandRef: CausalEstimandRef
  availableDataRegimeRefs
  causalAssumptionRefs
  modelOrDiagramRefs?
  calculusOrDerivationMethodRef?
  status: identified | bounded | nonidentified | unclear
  identifyingExpressionOrDerivationRef?   # required when identified
  boundResultRef?                         # required when bounded
  obstructionOrFailureWitnessRef?         # required when nonidentified
  falsificationOrNegativeControlRef?
  sensitivityAnalysisRef?
  supportedUse
  unsupportedUse

An identified label without an identifying expression or derivation is incomplete. A bounded result cites the bound. A nonidentified result exposes the obstruction or failure witness. Identification is neither a numerical estimate nor direct physical sampling.

Replayable identified case. For treatment_effect_in_population_P, AdjustmentSet_Z is justified as blocking the relevant back-door paths. backdoor_adjustment_derivation_7 states the identifying expression in ordinary terms: compare treated and untreated outcomes within each Z group, then average those differences using the target population’s Z distribution. The result cites the data regime, assumptions, expression, and the confounding or overlap change that would reopen it.

Replayable nonidentified case. In a treatment cohort, unmeasured severity affects both treatment and outcome, and no valid adjustment set, instrument, proxy, or useful bound is available. unmeasured_severity_obstruction_3 is the failure witness. The result is nonidentified; reporting an adjusted number does not change that status.

For a supplied causal model, C.28.MR derives the consequence by replacing the selected mechanism, retaining the other mechanisms and input law, and solving the relations needed by the query. The following case gives its small observation/intervention entry.

Replayable sensor case: observation and intervention. Let H denote binary high load and S a binary alarm. Stipulate P(H=1)=0.5, P(S=1|H=1)=0.9 and P(S=1|H=0)=0.1. Bayes’ rule gives P(H=1|S=1)=0.9 and P(H=1|S=0)=0.1. These are observational questions about the stated joint distribution.

For the query P(H=1|do(S=0)), additionally specify a structural model: H is determined by an exogenous random input; S is a noisy measurement of H with separate independent noise; S has no influence on H. Replacing the S mechanism by the constant zero preserves the H mechanism and its input distribution, giving P(H=1|do(S=0))=0.5. This derivation is an identified model-based result under those assumptions. The corrected Pearl, Glymour and Jewell primer, p.55 explains the mechanism-replacement operation.

If the alarm controls cooling, specify the intervention time and the subsequent load mechanism before answering a later-load question. F.0.2:5.5 uses this distinction when comparing source theories for an explanation.