Causality¶
Pearl, J. (2009). Causality: Models, Reasoning, and Inference. Cambridge University Press.
Cited by¶
25 citations across 24 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Aggregation
- Aggregation prompts reasoning about what is lost, whose perspective survives, and how distortion is introduced under compression—questions central to Pearl's (2009) causal-inference treatment of confounding, collapsibility, and the failure of marginal associations to track conditional structure.
This sourceCausal-inference treatment of confounding, collapsibility, and Simpson's paradox (Ch. 6); supports the claim that aggregation invites reasoning about distortion, lost perspective, and the failure of marginal associations to track conditional structure.
- Aggregation prompts reasoning about what is lost, whose perspective survives, and how distortion is introduced under compression—questions central to Pearl's (2009) causal-inference treatment of confounding, collapsibility, and the failure of marginal associations to track conditional structure.
- Black Box vs. White Box Distinction
- In causal inference and applied statistics, Pearl's Causality: Models, Reasoning, and Inference
This sourceDevelops structural causal models, directed acyclic graphs, and the do-calculus: answering interventional/counterfactual questions requires opening the box to a white-box causal structure rather than black-box correlation.
- Pearl's work on causality (2009)
This sourceFormalizes that correlation (black-box observation) cannot answer causal questions without white-box structural specification and the do-operator.
- In causal inference and applied statistics, Pearl's Causality: Models, Reasoning, and Inference
- Causality
- Scientific methodology deploys causal inference across randomized controlled trials (RCTs assign treatment randomly to eliminate confounding), instrumental variables (identifying causal effects when randomization is infeasible by leveraging quasi-exogenous variation), regression discontinuity (extracting causal effects at a threshold), and Judea Pearl's do-calculus — a formal machinery for identifying which causal parameters are identifiable from observational data under explicit assumptions about the underlying causal graph.
This sourceCanonical formalization of structural causal models, the do-operator, do-calculus, the DAG factorization P(V)=∏ᵢ P(Vᵢ|pa(Vᵢ)), and the observational-vs-interventional distinction P(Y|X=x) vs. P(Y|do(X=x)).
- Scientific methodology deploys causal inference across randomized controlled trials (RCTs assign treatment randomly to eliminate confounding), instrumental variables (identifying causal effects when randomization is infeasible by leveraging quasi-exogenous variation), regression discontinuity (extracting causal effects at a threshold), and Judea Pearl's do-calculus — a formal machinery for identifying which causal parameters are identifiable from observational data under explicit assumptions about the underlying causal graph.
- Ceteris Paribus
- In causal inference it is the interventionist conception of cause, holding other variables fixed while intervening on the target, and the closest-possible-world semantics of counterfactuals.
This sourceFormalizes the interventionist do-operator (holding other variables fixed while intervening on a target) and the closest-possible-world semantics of counterfactuals.
- In causal inference it is the interventionist conception of cause, holding other variables fixed while intervening on the target, and the closest-possible-world semantics of counterfactuals.
- Confounding
- The back-door path in the causal graph
This sourceCanonical modern formalization of causal inference; develops the back-door criterion and d-separation for graph-based confounder identification (supports D25-017, D25-018, D25-022, D25-024, D25-029).
- The back-door path in the causal graph
- Correlation
- It motivates the whole apparatus built to upgrade a correlation into a causal claim — randomization, instrumental variables, controlling for confounders, and the do-calculus of Pearl (2009), which makes formally explicit the gap between observing P(Y | X) and intervening to set P(Y | do(X)).
This sourceCanonical modern reference for causal inference; the do-calculus makes formally explicit the gap between observing P(Y | X) and intervening to set P(Y | do(X)), i.e., between correlation and causation.
- It motivates the whole apparatus built to upgrade a correlation into a causal claim — randomization, instrumental variables, controlling for confounders, and the do-calculus of Pearl (2009), which makes formally explicit the gap between observing P(Y | X) and intervening to set P(Y | do(X)).
- Counterfactual Reasoning
This sourceFormal structural-causal-model treatment of counterfactual truth-conditions via interventions; cited for the metaphysical/semantic side contrasted with the cognitive process (Tension T3).
- Counterfactuals
- Pearl (2009)
This sourceReframes counterfactuals as interventions on structural causal models via the do-operator and graph surgery, sidestepping possible-worlds similarity. Verified support for the do-operator reframing, the structural-model route around nearest-world identification, and the non-reductive view of causation.
- Pearl (2009)
- Directed Acyclic Graph
- Causal inference uses directed acyclic graphs of cause-before-effect, where a cycle would imply backward causation, and probabilistic graphical models factor joint distributions along such graphs.
This sourceCausal DAGs, do-calculus over descendants, and the prohibition of cycles (backward causation).
- Causal inference uses directed acyclic graphs of cause-before-effect, where a cycle would imply backward causation, and probabilistic graphical models factor joint distributions along such graphs.
- Factorization
- The structural payoff is the prime's signature move, intervention-as-replace-one-factor: a \(do(X_3 = x)\) intervention deletes the single factor \(P\(X_3 \mid \text{parents}\)\) and substitutes a point mass, leaving every other factor untouched — which is exactly why a factored causal model supports counterfactual reasoning that an unfactored joint table cannot.
This sourceEstablishes factorization of the joint over a causal DAG into local mechanisms so that a do-intervention replaces a single factor while leaving the others untouched, supporting counterfactual reasoning.
- The structural payoff is the prime's signature move, intervention-as-replace-one-factor: a \(do(X_3 = x)\) intervention deletes the single factor \(P\(X_3 \mid \text{parents}\)\) and substitutes a point mass, leaving every other factor untouched — which is exactly why a factored causal model supports counterfactual reasoning that an unfactored joint table cannot.
- Impartiality
- Pearl's (2009) graphical-causal framework makes this precise — counterfactual impartiality becomes the requirement that the protected attribute have no causal path to the prediction except through legitimately relevant mediators.
This sourceCanonical modern reference for causal-inference formalization. Earlier: Pearl, Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference (San Mateo, CA: Morgan Kaufmann, 1988). Accessible: Pearl, Judea, Madelyn Glymour, and Nicholas P. Jewell, Causal Inference in Statistics: A Primer (Chichester: Wiley, 2016).
- Pearl's (2009) graphical-causal framework makes this precise — counterfactual impartiality becomes the requirement that the protected attribute have no causal path to the prediction except through legitimately relevant mediators.
- Intervention
- The do-calculus makes the contrast vivid: conditioning on an observed value leaves the rest of the dependency structure intact, so the variable's relation to an outcome may be confounded by common causes, whereas intervening forces the value and cuts the incoming arrows, leaving the only path to the outcome through the variable's own outgoing edges and purging confounding.
This sourceDefines the do-operator and do-calculus — intervention as severing a variable's incoming edges while retaining outgoing ones — and the back-door/front-door criteria for identifying interventional from observational distributions.
- The do-calculus makes the contrast vivid: conditioning on an observed value leaves the rest of the dependency structure intact, so the variable's relation to an outcome may be confounded by common causes, whereas intervening forces the value and cuts the incoming arrows, leaving the only path to the outcome through the variable's own outgoing edges and purging confounding.
- Markov Blanket
- And in statistical control, a sufficient adjustment set is the causal-inference cousin, a blanket that screens off confounding paths.
This sourceDevelops sufficient adjustment sets and the back-door criterion, the causal-inference cousin of the Markov blanket that screens off confounding paths.
- And in statistical control, a sufficient adjustment set is the causal-inference cousin, a blanket that screens off confounding paths.
- Minimal Modification Principle
- Minimal modification provides a principled way to identify the counterfactual scenario (or the minimal set of them), making reasoning tractable, as Pearl (2009) operationalizes through structural causal models and the do-calculus.
This sourceDevelops structural causal models and the do-calculus, operationalizing minimal modification computationally: an intervention do(X = x) modifies only X while preserving the rest of the causal model, yielding tractable counterfactual reasoning.
- Minimal modification provides a principled way to identify the counterfactual scenario (or the minimal set of them), making reasoning tractable, as Pearl (2009) operationalizes through structural causal models and the do-calculus.
- Path
- In causal reasoning a causal path traces a directed sequence of cause-to-effect through a structural graph, and identifying and blocking such paths is how interventions are computed.
This sourceDevelops causal paths through structural graphs, back-door paths and confounding, and blocking paths by conditioning to identify effects.
- In causal reasoning a causal path traces a directed sequence of cause-to-effect through a structural graph, and identifying and blocking such paths is how interventions are computed.
- Relation
- Causal structure is additional content not encoded in the relation itself, requiring directionality, counterfactual support, and mechanism
This sourceCanonical modern reference for causal-inference formalization. Earlier: Pearl, Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference (San Mateo, CA: Morgan Kaufmann, 1988). Accessible: Pearl, Judea, Madelyn Glymour, and Nicholas P. Jewell, Causal Inference in Statistics: A Primer (Chichester: Wiley, 2016).
- Causal structure is additional content not encoded in the relation itself, requiring directionality, counterfactual support, and mechanism
- Simpson–Yule Effect
- The structural test is uniform and would have exposed this in advance: stratify by the candidate confounder and recompute.
This sourceEstablishes the causal resolution of Simpson's paradox — whether to condition depends on the causal role (confounder vs. mediator), via the back-door criterion — and the stratify-by-the-confounder test.
- The structural test is uniform and would have exposed this in advance: stratify by the candidate confounder and recompute.
- Simpson's Paradox
- Confounder-adjustment frameworks in causal inference — DAGs, do-calculus — are the formal apparatus around the paradox, and a Simpson reversal is one signature output of an uncontrolled confounder.
This sourceThe formal causal-inference apparatus (DAGs, do-calculus) within which Simpson's paradox is resolved by adjusting for the confounder; a sign reversal on stratification signals an uncontrolled confounder.
- Confounder-adjustment frameworks in causal inference — DAGs, do-calculus — are the formal apparatus around the paradox, and a Simpson reversal is one signature output of an uncontrolled confounder.
- Statistical Inference
- Causal inference: Do-calculus (Pearl, 2009), the back-door and front-door criteria, instrumental variables, regression discontinuity, matching and propensity scores, difference-in-differences, synthetic control methods.
This sourceCanonical modern reference for causal-inference formalization. Earlier: Pearl, Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference (San Mateo, CA: Morgan Kaufmann, 1988). Accessible: Pearl, Judea, Madelyn Glymour, and Nicholas P. Jewell, Causal Inference in Statistics: A Primer (Chichester: Wiley, 2016).
- Causal inference: Do-calculus (Pearl, 2009), the back-door and front-door criteria, instrumental variables, regression discontinuity, matching and propensity scores, difference-in-differences, synthetic control methods.
- Temporal Dynamics
- This prime names systems where temporal structure is load-bearing, a distinction Pearl (2009) develops in his framework separating the temporal medium of causal flow from the structural patterns that exploit it.
This sourceCanonical modern reference for causal-inference formalization. Earlier: Pearl, Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference (San Mateo, CA: Morgan Kaufmann, 1988). Accessible: Pearl, Judea, Madelyn Glymour, and Nicholas P. Jewell, Causal Inference in Statistics: A Primer (Chichester: Wiley, 2016).
- This prime names systems where temporal structure is load-bearing, a distinction Pearl (2009) develops in his framework separating the temporal medium of causal flow from the structural patterns that exploit it.
- Underspecification
- In causal inference, multiple causal graphs imply the same conditional independences, and the data alone cannot adjudicate; the one finally drawn reflects modeling convention rather than evidence.
This sourceDevelops Markov equivalence classes — distinct causal graphs implying identical conditional independences that observational data alone cannot adjudicate.
- In causal inference, multiple causal graphs imply the same conditional independences, and the data alone cannot adjudicate; the one finally drawn reflects modeling convention rather than evidence.
Domain-specific¶
Mechanisms¶
- D-Separation Walkthrough
- The classic misuse is the covariate reflex — conditioning on everything measurable "to be safe," which d-separation shows can open collider paths
This sourceShows that conditioning on a collider or its descendant can unblock a path and induce dependence between previously independent causes.
- The classic misuse is the covariate reflex — conditioning on everything measurable "to be safe," which d-separation shows can open collider paths
Verification¶
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Links previously used in the corpus¶
Before the registry existed this work was also linked 2 other ways.
- https://www.cambridge.org/core/books/causality/B0046844FAE10CBF274D4ACBDAEB5F5B ×2
- https://bayes.cs.ucla.edu/BOOK-2K/ ×1
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