Working definition
Causal inference asks how an outcome would differ under alternative interventions, using a declared causal graph, identification assumptions, and study design. Randomization can identify effects under compliance and measurement conditions; observational analyses require stronger, testable and untestable assumptions.
Notation
ATE = E[Y(1) − Y(0)]Y ⟂ T | X under conditional exchangeabilityAssumptions
- Treatment, outcome, and intervention are well defined.
- Confounders required for identification are addressed.
- Interference and selection are considered.
Invariants
- Association alone does not identify intervention effect.
- Adjustment follows the causal graph rather than predictive importance.
- A counterfactual contrast requires a target population.
Reproducible procedure
- Draw the assumed causal structure.
- Choose a design and identification strategy.
- Estimate effects with falsification and sensitivity analyses.
Error and boundary controls
- Unmeasured confounding may dominate.
- Positivity failures prevent comparison.
- Measurement and selection bias can reverse estimates.
What this does not establish
Unless celestial timing is manipulated or otherwise identified under a defensible design, predictive association must not be described as celestial causation.
Explicit applications
1 cross-domain bridges
Prediction-versus-causation boundary
Specify when a benchmark can support predictive skill and why it usually cannot identify celestial causation.
Inputs
- study design
- assignment mechanism
- outcomes and covariates
Outputs
- supported claim type
- unidentified paths
- sensitivity analysis
Transformation: Map identification assumptions and test observable implications.
Limit: Most observational celestial-timing studies can test incremental prediction, not physical causation.
Open connected system →Authoritative references
- [1]NIST/SEMATECH e-Handbook of Statistical Methods · National Institute of Standards and Technology
Establishes: Methods for uncertainty analysis, calibration, time-series modeling, process monitoring, experimental design, reliability, and statistical comparison.
Boundary: Statistical procedures quantify evidence under a design and model; they do not repair biased sampling, outcome leakage, post-hoc hypotheses, or unmeasured confounding.
Direct answer
- Causal inference asks how an outcome would differ under alternative interventions, using a declared causal graph, identification assumptions, and study design. Randomization can identify effects under compliance and measurement conditions; observational analyses require stronger, testable and untestable assumptions.
Mechanism and method
- Draw the assumed causal structure.
- Choose a design and identification strategy.
- Estimate effects with falsification and sensitivity analyses.
What is measured
- Association alone does not identify intervention effect.
- Adjustment follows the causal graph rather than predictive importance.
- A counterfactual contrast requires a target population.
Limitations
- Unmeasured confounding may dominate.
- Positivity failures prevent comparison.
- Measurement and selection bias can reverse estimates.
- Treatment, outcome, and intervention are well defined.
- Confounders required for identification are addressed.
- Interference and selection are considered.
What this does not establish
- Unless celestial timing is manipulated or otherwise identified under a defensible design, predictive association must not be described as celestial causation.
Bridge: Prediction-versus-causation boundary
- Specify when a benchmark can support predictive skill and why it usually cannot identify celestial causation.
- Input: study design
- Input: assignment mechanism
- Input: outcomes and covariates
- Output: supported claim type
- Output: unidentified paths
- Output: sensitivity analysis
- Limit: Most observational celestial-timing studies can test incremental prediction, not physical causation.