Causality¶
Pearl, J. (2009). Causality: Models, Reasoning, and Inference. Cambridge University Press.
Cited by¶
36 citations across 35 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.
Supported in partVerified against the publisher's abstract
The book's abstract supports only that Pearl builds tools relating causal connections to statistical associations; it says nothing about aggregation, lost perspective, collapsibility, or Simpson's paradox.
“devises simple mathematical tools for studying the relationships between causal connections and statistical associations”
- 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.
SupportedVerified against the publisher's abstract
The publisher abstract describes the book as a comprehensive exposition of causal analysis with applications in statistics, supporting its placement in causal inference and applied statistics.
“this book provides a comprehensive exposition of modern analysis of causation. It shows how causality has grown from a nebulous concept into a mathematical theory with significant applications in the fields of statistics”
- 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.
Supported in partVerified against the publisher's abstract
The publisher abstract confirms Pearl's 2009 Causality treats structural approaches to causation, but does not itself state that correlation cannot answer causal questions without a white-box specification.
“Judea Pearl presents and unifies the probabilistic, manipulative, counterfactual, and structural approaches to causation and devises simple mathematical tools for studying the relationships between causal connections and statistical associations.”
- In causal inference and applied statistics, Pearl's Causality: Models, Reasoning, and Inference
- Causal reasoning
- 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)).
Supported in partVerified against the publisher's abstract
Pearl's book grounds the do-calculus clause as formal machinery for causal analysis; the abstract says nothing of RCTs, instrumental variables, or regression discontinuity.
“Judea Pearl presents and unifies the probabilistic, manipulative, counterfactual, and structural approaches to causation and devises simple mathematical tools for studying the relationships between causal connections and statistical associations.”
- 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.
Supported in partVerified against the publisher's abstract
The book's abstract confirms a monograph unifying manipulative (interventionist) and counterfactual approaches to causation; it says nothing about the single-market comparative-statics clause of the anchor.
“Judea Pearl presents and unifies the probabilistic, manipulative, counterfactual, and structural approaches to causation and devises simple mathematical tools for studying the relationships between causal connections and statistical associations.”
- 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).
Supported in partVerified against the publisher's abstract
Pearl's own publisher description places the book at the relation between causal connections and statistical associations, supporting the frame of a spurious-association mechanism but not stating that mechanism.
“Judea Pearl presents and unifies the probabilistic, manipulative, counterfactual, and structural approaches to causation and devises simple mathematical tools for studying the relationships between causal connections and statistical associations.”
- 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.
Supported in partVerified against the publisher's abstract
The publisher abstract backs only the frame — mathematical tools relating causal connections to statistical associations — and never names the do-calculus or P(Y | do(X)), so the sentence's specific formulation stays unverified.
“Judea Pearl presents and unifies the probabilistic, manipulative, counterfactual, and structural approaches to causation and devises simple mathematical tools for studying the relationships between causal connections and statistical associations.”
- 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.
Supported in partVerified against the publisher's abstract
Pearl's Causality is the book that unifies the counterfactual and structural approaches to causation; the abstract confirms the attribution but never states the do-operator or the sidestepping of possible-worlds similarity.
“Judea Pearl presents and unifies the probabilistic, manipulative, counterfactual, and structural approaches to causation and devises simple mathematical tools for studying the relationships between causal connections and statistical associations.”
- 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).
Supported in partVerified against the publisher's abstract
The publisher abstract confirms Pearl's *Causality* develops manipulative and structural tools for causal connections, but says nothing of induced order or of do-calculus tracing exactly the descendants of a manipulated node.
“Judea Pearl presents and unifies the probabilistic, manipulative, counterfactual, and structural approaches to causation and devises simple mathematical tools for studying the relationships between causal connections and statistical associations.”
- 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).
Supported in partVerified against the publisher's abstract
Pearl's own abstract confirms a unified counterfactual/structural causal framework, but says nothing about protected attributes, predictions, or mediators, so it carries only the framing half of the claim.
“Judea Pearl presents and unifies the probabilistic, manipulative, counterfactual, and structural approaches to causation and devises simple mathematical tools for studying the relationships between causal connections and statistical associations.”
- 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.
Supported in partVerified against the publisher's abstract
Pearl's abstract establishes the book as the work that builds the do-calculus tools linking causal to statistical relations, but nothing readable here supports the claim's randomized-trial clause.
“Judea Pearl presents and unifies the probabilistic, manipulative, counterfactual, and structural approaches to causation and devises simple mathematical tools for studying the relationships between causal connections and statistical associations.”
- 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.
Supported in partVerified against the publisher's abstract
The abstract confirms Pearl's Causality is a work on causal inference and statistical association, but it never mentions sufficient adjustment sets, the back-door criterion, or screening off confounding paths.
“Judea Pearl presents and unifies the probabilistic, manipulative, counterfactual, and structural approaches to causation and devises simple mathematical tools for studying the relationships between causal connections and statistical associations.”
- 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.
Supported in partVerified against the publisher's abstract
Pearl's book abstract confirms it unifies structural and counterfactual approaches to causation and devises mathematical tools, but it does not name minimal modification, the do-calculus, or unique counterfactual identification.
“Judea Pearl presents and unifies the probabilistic, manipulative, counterfactual, and structural approaches to causation and devises simple mathematical tools for studying the relationships between causal connections and statistical associations.”
- 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.
Supported in partVerified against the publisher's abstract
Pearl's Causality is the canonical structural-causal-modelling text, but the publisher abstract obtained here states only the general structural approach to causation, not the back-door/front-door path machinery the claim asserts.
“Judea Pearl presents and unifies the probabilistic, manipulative, counterfactual, and structural approaches to causation and devises simple mathematical tools for studying the relationships between causal connections and statistical associations.”
- 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).
Supported in partVerified against the publisher's abstract
Pearl's Causality is the canonical mathematical formalization of causation and supplies tools for causal inference, but this abstract names no do-calculus, no back-door/front-door criterion, and none of the other listed methods.
“Judea Pearl presents and unifies the probabilistic, manipulative, counterfactual, and structural approaches to causation and devises simple mathematical tools for studying the relationships between causal connections and statistical associations.”
- 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.
Borderline supportVerified against the publisher's abstract
The book's own abstract frames causation as a mathematical theory relating causal connections to statistical associations; it does not state Markov equivalence or ill-posedness.
“devises simple mathematical tools for studying the relationships between causal connections and statistical associations”
Two runs of the same check disagreed on this citation; the later verdict is shown and the citation is queued for review.
- 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¶
- Lord's Paradox
- The analyst infers causal structure from the instability of the conclusion under adjustment: sensitivity of the verdict to conditioning is evidence about the DAG, not noise to be explained away
This sourcePearl's Causality sets out that observationally equivalent DAGs are not distinguished by the data, so causal direction must be supplied from outside observational evidence.
Supported in partVerified against the work's full text
“technical term [identification]. 3.2 Intervention in Markovian Models 77 3.2.4 [Identification] of Causal”
- The analyst infers causal structure from the instability of the conclusion under adjustment: sensitivity of the verdict to conditioning is evidence about the DAG, not noise to be explained away
- Regression
- Crossing from prediction to causation without that external warrant is the field's canonical error.
This sourceA treatment of causal inference that distinguishes causal-effect identification from parameter identification in a fitted model and treats confounding and omitted factors as the obstacles to a causal reading.
Supported in partVerified against a saved copy of the source
“between parameter identification in linear models and causal effect identification in nonparametric”
- Crossing from prediction to causation without that external warrant is the field's canonical error.
- Sure-thing principle
Mechanisms¶
- Antecedent Edit Card
- Written as an intervention on one node, it matches the surgical logic of the do-operator in causal inference: set this variable, sever its ordinary causes, and leave the rest of the model in place.
This sourceDocuments Written as an intervention on one node; set this variable; sever its ordinary causes; leave the rest of the model in place.
- Written as an intervention on one node, it matches the surgical logic of the do-operator in causal inference: set this variable, sever its ordinary causes, and leave the rest of the model in place.
- Causal Diagram
- Causal Diagramming
- The discipline that guards against this is to derive the adjustment set from the diagram before touching outcome data — the back-door criterion makes that derivation explicit
This sourceDefines the back-door criterion as a graphical test for whether a covariate set blocks all paths entering the treatment through the back door.
- The discipline that guards against this is to derive the adjustment set from the diagram before touching outcome data — the back-door criterion makes that derivation explicit
- Common-Driver Decomposition
- Correlation is not common cause: things can move together because of a lurking third factor, and a decomposition run on correlations alone can crown a spurious driver.
This sourceShows that correlation need not identify causation because a common cause can induce association between its effects.
- Correlation is not common cause: things can move together because of a lurking third factor, and a decomposition run on correlations alone can crown a spurious driver.
- 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
- Event Knowledge Graph
- A `correlated-with` edge read as causation is the classic error — a suggestive path is a hypothesis, not evidence, and the graph will happily draw a compelling shape out of pure co-occurrence.
This sourceDistinguishes statistical association from causation and shows that causal conclusions require assumptions beyond observed co-occurrence.
- A `correlated-with` edge read as causation is the classic error — a suggestive path is a hypothesis, not evidence, and the graph will happily draw a compelling shape out of pure co-occurrence.
- Minimal Causal Diagram
- This is the standing hazard of causal DAGs
This sourceShows that an open back-door path represents confounding and can invalidate a causal effect estimate unless blocked.
- This is the standing hazard of causal DAGs
- Null-Model Residual Report
- Its failure mode is the seductive residual: a large departure from a null feels like a discovery, and readers routinely mistake "deviates from my model" for "was caused by the thing I care about," ignoring confounding.
This sourceDefines confounding as spurious association produced by extraneous variables that can bias a causal-effect estimate.
- Its failure mode is the seductive residual: a large departure from a null feels like a discovery, and readers routinely mistake "deviates from my model" for "was caused by the thing I care about," ignoring confounding.
- Post-Safeguard Incentive Audit
- Its honest limit is that it is a structural map, not a measurement: it can name where harm probably moved without sizing it, and a confident diagram can overstate its own certainty.
This sourceDistinguishes a qualitative causal structure from quantitative effect measurement, allowing a graph to identify pathways without sizing them.
- Its honest limit is that it is a structural map, not a measurement: it can name where harm probably moved without sizing it, and a confident diagram can overstate its own certainty.
- Relevance and Alternative Explanation Check
- This is the everyday face of confounding.
This sourceDefines confounding as a mismatch between observational association and the causal response under intervention.
- This is the everyday face of confounding.
Verification¶
Does it exist? Confirmed. This work's DOI resolves to a registered record, which fixes its identity. That is all it fixes.
Does it back the claim? Read against the text for 18 of 36 citations: 1 supported, 16 supported in part, 1 borderline. Each verdict is shown under its citation below, with what in the work backs the sentence.
Support is checked per citation rather than per work — the same source can be cited soundly in one article and wrongly in another. Per-citation recording began recently, so a citation with no recorded check is a gap in the record rather than evidence it went unchecked.
See how references were verified.
Links previously used in the corpus¶
Before the registry existed this work was also linked 3 other ways.
- https://www.cambridge.org/core/books/causality/B0046844FAE10CBF274D4ACBDAEB5F5B ×3
- https://bayes.cs.ucla.edu/BOOK-2K/ ×2
- https://search.worldcat.org/title/1005653753 ×1
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