67:
25:
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data alone, without the need for an experimental intervention, which might be expensive, lengthy or even unethical (e.g., asking subjects to take up smoking). The set of rules is complete (it can be used to derive every true statement in this system). An algorithm can determine whether, for a given model, a solution is computable in
5517:
conclusions can be drawn from an incomplete dataset. In some cases, data from studies of multiple populations can be combined (via transportation) to allow conclusions about an unmeasured population. In some cases, combining estimates (e.g., P(W|X)) from multiple studies can increase the precision of a conclusion.
369:, but once it became a rote method, it lost its utility, leading some practitioners to reject any relationship to causality. Economists adopted the algebraic part of path analysis, calling it simultaneous equation modeling. However, economists still avoided attributing causal meaning to their equations.
4600:
For linear models, the indirect effect can be computed by taking the product of all the path coefficients along a mediated pathway. The total indirect effect is computed by the sum of the individual indirect effects. For linear models mediation is indicated when the coefficients of an equation fitted
760:
Counterfactuals can indicate the existence of a causal relationship. Models that can answer counterfactuals allow precise interventions whose consequences can be predicted. At the extreme, such models are accepted as physical laws (as in the laws of physics, e.g., inertia, which says that if force is
647:
The highest level, counterfactual, involves consideration of an alternate version of a past event, or what would happen under different circumstances for the same experimental unit. For example, what is the probability that, if a store had doubled the price of floss, the toothpaste-purchasing shopper
406:
introduced the "exchangeability" approach to handling confounding by considering a counterfactual. They proposed assessing what would have happened to the treatment group if they had not received the treatment and comparing that outcome to that of the control group. If they matched, confounding was
5520:
Do-calculus provides a general criterion for transport: A target variable can be transformed into another expression via a series of do-operations that does not involve any "difference-producing" variables (those that distinguish the two populations). An analogous rule applies to studies that have
4971:
Indirect effects cannot be "controlled" because the direct path cannot be disabled by holding another variable constant. The natural indirect effect (NIE) is the effect on gum health (Y) from flossing (M). The NIE is calculated as the sum of (floss and no-floss cases) of the difference between the
2928:
If the backdoor criterion is satisfied for (X,Y), X and Y are deconfounded by the set of confounder variables. It is not necessary to control for any variables other than the confounders. The backdoor criterion is a sufficient but not necessary condition to find a set of variables Z to decounfound
5535:
Any causal model can be implemented as a
Bayesian network. Bayesian networks can be used to provide the inverse probability of an event (given an outcome, what are the probabilities of a specific cause). This requires preparation of a conditional probability table, showing all possible inputs and
3777:
The do calculus is the set of manipulations that are available to transform one expression into another, with the general goal of transforming expressions that contain the do operator into expressions that do not. Expressions that do not include the do operator can be estimated from observational
419:
involves a three-level abstraction he calls the ladder of causation. The lowest level, Association (seeing/observing), entails the sensing of regularities or patterns in the input data, expressed as correlations. The middle level, Intervention (doing), predicts the effects of deliberate actions,
2912:
For analysing the causal effect of X on Y in a causal model all confounder variables must be addressed (deconfounding). To identify the set of confounders, (1) every noncausal path between X and Y must be blocked by this set; (2) without disrupting any causal paths; and (3) without creating any
5603:
A different conceptualization of causality involves the notion of invariant relationships. In the case of identifying handwritten digits, digit shape controls meaning, thus shape and meaning are the invariants. Changing the shape changes the meaning. Other properties do not (e.g., color). This
4436:
Examining a counterfactual using a causal model involves three steps. The approach is valid regardless of the form of the model relationships, linear or otherwise. When the model relationships are fully specified, point values can be computed. In other cases (e.g., when only probabilities are
144:
Causal models are mathematical models representing causal relationships within an individual system or population. They facilitate inferences about causal relationships from statistical data. They can teach us a good deal about the epistemology of causation, and about the relationship between
535:
This level asserts specific causal relationships between events. Causality is assessed by experimentally performing some action that affects one of the events. Example: after doubling the price of toothpaste, what would be the new probability of purchasing? Causality cannot be established by
5516:
Where two models match on all relevant variables and data from one model is known to be unbiased, data from one population can be used to draw conclusions about the other. In other cases, where data is known to be biased, reweighting can allow the dataset to be transported. In a third case,
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Queries are questions asked based on a specific model. They are generally answered via performing experiments (interventions). Interventions take the form of fixing the value of one variable in a model and observing the result. Mathematically, such queries take the form (from the example):
4094:
The rules do not imply that any query can have its do operators removed. In those cases, it may be possible to substitute a variable that is subject to manipulation (e.g., diet) in place of one that is not (e.g., blood cholesterol), which can then be transformed to remove the do. Example:
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An essential element of correlational study design is to identify potentially confounding influences on the variable under study, such as demographics. These variables are controlled for to eliminate those influences. However, the correct list of confounding variables cannot be determined
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invariance should carry across datasets generated in different contexts (the non-invariant properties form the context). Rather than learning (assessing causality) using pooled data sets, learning on one and testing on another can help distinguish variant from invariant properties.
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Independence conditions are rules for deciding whether two variables are independent of each other. Variables are independent if the values of one do not directly affect the values of the other. Multiple causal models can share independence conditions. For example, the models
5508:
Causal models provide a vehicle for integrating data across datasets, known as transport, even though the causal models (and the associated data) differ. E.g., survey data can be merged with randomized, controlled trial data. Transport offers a solution to the question of
316:
time and litter size. Opposition to these ideas by prominent statisticians led them to be ignored for the following 40 years (except among animal breeders). Instead scientists relied on correlations, partly at the behest of Wright's critic (and leading statistician),
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Causal models offer a robust technique for identifying appropriate confounding variables. Formally, Z is a confounder if "Y is associated with Z via paths not going through X". These can often be determined using data collected for other studies. Mathematically, if
638:
is an operator that signals the experimental intervention (doubling the price). The operator indicates performing the minimal change in the world necessary to create the intended effect, a "mini-surgery" on the model with as little change from reality as possible.
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In experiments on such a model, the controlled direct effect (CDE) is computed by forcing the value of the mediator M (do(M = 0)) and randomly assigning some subjects to each of the values of X (do(X=0), do(X=1), ...) and observing the resulting values of Y.
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operator indicates that the experiment explicitly modified the price of toothpaste. Graphically, this blocks any causal factors that would otherwise affect that variable. Diagramatically, this erases all causal arrows pointing at the experimental variable.
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visits (X) from every other year to every year, which encourages flossing (M). Gums (Y) get healthier, either because of the hygienist (direct) or the flossing (mediator/indirect). The experiment is to continue flossing while skipping the hygienist visit.
2925:: Given an ordered pair of variables (X,Y) in a model, a set of confounder variables Z satisfies the backdoor criterion if (1) no confounder variable Z is a descendent of X and (2) all backdoor paths between X and Y are blocked by the set of confounders.
2181:
Regression coefficients can serve as estimates of the causal effect of an instrumental variable on an outcome as long as that effect is not confounded. In this way, instrumental variables allow causal factors to be quantified without data on confounders.
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Traditionally, B was considered to be a confounder, because it is associated with X and with Y but is not on a causal path nor is it a descendant of anything on a causal path. Controlling for B causes it to become a confounder. This is known as M-bias.
2616:
Conditioning on a variable is a mechanism for conducting hypothetical experiments. Conditioning on a variable involves analyzing the values of other variables for a given value of the conditioned variable. In the first example, conditioning on
4302:
The conventional approach to potential outcomes is data-, not model-driven, limiting its ability to untangle causal relationships. It treats causal questions as problems of missing data and gives incorrect answers to even standard scenarios.
526:
of the two events. Associations have no causal implications. One event could cause the other, the reverse could be true, or both events could be caused by some third event (unhappy hygienist shames shopper into treating their mouth better ).
383:
advocated replacing correlation with but-for causality (counterfactuals). He referred to humans' ability to envision alternative worlds in which a cause did or not occur, and in which an effect appeared only following its cause. In 1974
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the equations for calculating the values of A and C derived from regression analysis or another technique can be applied, substituting known values from an observation and fixing the value of other variables (the counterfactual).
120:(whether results from one study apply to unstudied populations). Causal models can allow data from multiple studies to be merged (in certain circumstances) to answer questions that cannot be answered by any individual data set.
257:
as the metric of association. He wrote, "Force as a cause of motion is exactly the same as a tree god as a cause of growth" and that causation was only a "fetish among the inscrutable arcana of modern science". Pearson founded
1052:
represents the values of those variables in a specific context. However, the required set of background variables is indeterminate (multiple sets may increase the probability), as long as probability is the only criterion.
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755:
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Because genes vary randomly across populations, presence of a gene typically qualifies as an instrumental variable, implying that in many cases, causality can be quantified using regression on an observational study.
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Refinements to the technique include creating an instrument by conditioning on other variable to block the paths between the instrument and the confounder and combining multiple variables to form a single instrument.
5324:
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Counterfactuals consider possibilities that are not found in data, such as whether a nonsmoker would have developed cancer had they instead been a heavy smoker. They are the highest step on Pearl's causality ladder.
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Presuming data for these observable probabilities is available, the ultimate probability can be computed without an experiment, regardless of the existence of other confounding paths and without backdoor adjustment.
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However, a better experiment is to compute the natural direct effect. (NDE) This is the effect determined by leaving the relationship between X and M untouched while intervening on the relationship between X and Y.
4788:
4551:
Direct and indirect (mediated) causes can only be distinguished via conducting counterfactuals. Understanding mediation requires holding the mediator constant while intervening on the direct cause. In the model
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When the causal model is a plausible representation of reality and the backdoor criterion is satisfied, then partial regression coefficients can be used as (causal) path coefficients (for linear relationships).
2230:
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778:, associations without any implied causal relationships. Causal models attempt to extend this framework by adding the notion of causal relationships, in which changes in one variable cause changes in others.
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examining history (of price changes) because the price change may have been for some other reason that could itself affect the second event (a tariff that increases the price of both goods). Mathematically:
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Causal diagrams are independent of the quantitative probabilities that inform them. Changes to those probabilities (e.g., due to technological improvements) do not require changes to the model.
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may be used in the development of a causal model. Causal models can improve study designs by providing clear rules for deciding which independent variables need to be included/controlled for.
1227:). Each node is connected by an arrow to one or more other nodes upon which it has a causal influence. An arrowhead delineates the direction of causality, e.g., an arrow connecting variables
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While this is tractable for small problems, as the number of variables and their associated states increase, the probability table (and associated computation time) increases exponentially.
5135:
398:
In 1986 Baron and Kenny introduced principles for detecting and evaluating mediation in a system of linear equations. As of 2014 their paper was the 33rd most-cited of all time. That year
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works for all model relationships (linear and nonlinear). It allows NDE to then be calculated directly from observational data, without interventions or use of counterfactual subscripts.
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causation and probability. They have also been applied to topics of interest to philosophers, such as the logic of counterfactuals, decision theory, and the analysis of actual causation.
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219:. At one point, he denied that objects have "powers" that make one a cause and another an effect. Later he adopted "if the first object had not been, the second had never existed" ("
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424:(imagining), involves constructing a theory of (part of) the world that explains why specific actions have specific effects and what happens in the absence of such actions.
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The indirect effect of X on Y is the "increase we would see in Y while holding X constant and increasing M to whatever value M would attain under a unit increase in X".
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whose values are determined by factors outside the model; V is a set of endogenous variables whose values are determined by factors within the model; and E is a set of
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In the late 19th century, the discipline of statistics began to form. After a years-long effort to identify causal rules for domains such as biological inheritance,
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independent. However, the two models do not have the same meaning and can be falsified based on data (that is, if observational data show an association between
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2613:, then both models are incorrect). Conversely, data cannot show which of these two models are correct, because they have the same independence conditions.
924:) can satisfy the condition. Causality is relevant to the second ladder step. Associations are on the first step and provide only evidence to the latter.
2697:. If such a dependence exists, then the model is incorrect. Non-causal models cannot make such distinctions, because they do not make causal assertions.
2065:
A mediator node modifies the effect of other causes on an outcome (as opposed to simply affecting the outcome). For example, in the chain example above,
113:. Some interventional studies are inappropriate for ethical or practical reasons, meaning that without a causal model, some hypotheses cannot be tested.
4597:
The
Mediation Fallacy instead involves conditioning on the mediator if the mediator and the outcome are confounded, as they are in the above model.
2939:
376:
et al.'s critique, which objected that it handled only linear relationships and that robust, model-free presentations of data were more revealing.
310:
coat patterns. He backed up his then-heretical claims by showing how such analyses could explain the relationship between guinea pig birth weight,
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Noncollapsibility: A difference between the "crude relative risk and the relative risk resulting after adjustment for the potential confounder".
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proposed that any factor that is "causally relevant" to an effect be conditioned on, moving beyond simple probability as the only guide.
215:
defined a taxonomy of causality, including material, formal, efficient and final causes. Hume rejected
Aristotle's taxonomy in favor of
774:
Statistics revolves around the analysis of relationships among multiple variables. Traditionally, these relationships are described as
1072:) can be assessed by measuring the ability to predict the future values of one time series using prior values of another time series.
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109:
They can allow some questions to be answered from existing observational data without the need for an interventional study such as a
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542:
4515:, the proxy for the unobserved variables on the specific observation that supports the counterfactual. Compute the probability of
5539:
For example, given a two variable model of
Disease and Test (for the disease) the conditional probability table takes the form:
522:
or the probability of (purchasing) floss given (the purchase of) toothpaste. Associations can also be measured via computing the
442:
6236:
4594:
M mediates X's influence on Y, while X also has an unmediated effect on Y. Thus M is held constant, while do(X) is computed.
3456:
The following converts a do expression into a do-free expression by conditioning on the variables along the front-door path.
1667:
4557:
3060:
If the elements of a blocking path are all unobservable, the backdoor path is not calculable, but if all forward paths from
6383:
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The calculus includes three rules for the transformation of conditional probability expressions involving the do operator.
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Epidemiological: A variable associated with X in the population at large and associated with Y among people unexposed to X.
3462:
343:
warned that controlling for a variable Z is valid only if it is highly unlikely to be affected by independent variables.
2710:. It is thus possible that a study may control for irrelevant variables or even (indirectly) the variable under study.
2395:
uses measured variation in genes of known function to examine the causal effect of a modifiable exposure on disease in
436:
of observing the other. Example: shoppers who buy toothpaste are more likely to also buy dental floss. Mathematically:
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expunged the notion of causality from much of science as an unprovable special case of association and introduced the
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6045:
6004:
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and others rediscovered path analysis. While reading
Blalock's work on path diagrams, Duncan remembered a lecture by
6197:
Mendelian
Randomization: Genetic Variants as Instruments for Strengthening Causal Inference in Observational Studies
4183:{\displaystyle P({\text{Heart disease}}|do({\text{blood cholesterol}}))=P({\text{Heart disease}}|do({\text{diet}}))}
329:) and to assert that holding a mediator constant induces errors. She may have invented path diagrams independently.
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4978:
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More complex queries are possible, in which the do operator is applied (the value is fixed) to multiple variables.
336:
introduced the concept of a potential outcome, but his paper was not translated from Polish to
English until 1990.
3906:
in the case that the variable set Z blocks all paths from W to Y and all arrows leading into X have been deleted.
204:
that express the value of each endogenous variable as a function of the values of the other variables in U and V.
5595:
Bayesian networks are used commercially in applications such as wireless data error correction and DNA analysis.
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Z matches the definition, but is a mediator, not a confounder, and is an example of controlling for the outcome.
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5490:{\displaystyle {\mathsf {Total\ effect}}(X=0\rightarrow X=1)=NDE(X=0\rightarrow X=1)-\ NIE(X=1\rightarrow X=0)}
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According to this table, when a patient does not have the disease, the probability of a positive test is 12%.
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A later definition attempted to address this ambiguity by conditioning on background factors. Mathematically:
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can be computed by modifying causal model M (by deleting arrows into X) and computing the outcome for some
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2720:
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In forks, one cause has multiple effects. The two effects have a common cause. There exists a (non-causal)
366:
280:
161:
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In the context of causal models, potential outcomes are interpreted causally, rather than statistically.
110:
4370:
2919:: a backdoor path from variable X to Y is any path from X to Y that starts with an arrow pointing to X.
1365:
The three types of connections of three nodes are linear chains, branching forks and merging colliders.
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Definition: A potential outcome for a variable Y is "the value Y would have taken for individual
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https://www.pymc.io/projects/examples/en/latest/causal_inference/interventional_distribution.html
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359:
325:, a student who in 1926 was the first to apply path diagrams to represent a mediating influence (
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Chains are straight line connections with arrows pointing from cause to effect. In this model,
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Sixty years after his first paper, Wright published a piece that recapitulated it, following
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1897:. This negative correlation has been called collider bias and the "explain-away" effect as
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does not apply because of anomalies such as threshold effects and binary values. However,
8:
4504:
2153:
A confounder node affects multiple outcomes, creating a positive correlation among them.
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introduced the notion of "potential outcomes" as a language for asking causal questions.
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For a specific observation, use the do operator to establish the counterfactual (e.g.,
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Rule 2 permits the replacement of an intervention with an observation or vice versa.:
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Such definitions are inadequate because other relationships (e.g., a common cause for
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without including the mediator vary significantly from an equation that includes it.
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124:
46:
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twenty years earlier that mentioned a paper by Wright that in turn mentioned Burks.
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Katan MB (March 1986). "Apolipoprotein E isoforms, serum cholesterol, and cancer".
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5679:"Causal Modelling and Brain Connectivity in Functional Magnetic Resonance Imaging"
302:. He developed this approach while attempting to untangle the relative impacts of
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235:
103:
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that uses observation to find the simplest/most likely explanation) to estimate
70:
Comparison of two competing causal models (DCM, GCM) used for interpretation of
6195:
3267:: a frontdoor path is a direct causal path for which data is available for all
1212:
227:
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6395:
6347:
6214:
5613:
3045:{\displaystyle P(Y|do(X))=\textstyle \sum _{z}\displaystyle P(Y|X,Z=z)P(Z=z)}
1357:
Causal models have formal structures with elements with specific properties.
373:
318:
291:
1957:. The correlation can be positive in the case where contributions from both
750:{\displaystyle P(\mathrm {floss} |\mathrm {toothpaste} ,2*\mathrm {price} )}
6365:
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5683:
5674:
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probability of flossing given the hygienist and without the hygienist, or:
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416:
403:
385:
333:
299:
250:
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128:
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Riegelman, R. (1979). "Contributory cause: Unnecessary and insufficient".
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is instead called sufficient. A contributory cause may also be necessary.
24:
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5319:{\displaystyle {\mathsf {Total\ effect=Direct\ effect+Indirect\ effect}}}
433:
272:
239:
155:
79:
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1331:
is a traversal of the graph between two nodes following causal arrows.
1116:
will occur. Necessary causes are also known as "but-for" causes, as in
805:) was said to cause another if it raises the probability of the other (
307:
260:
246:
6029:
5631:– a statistical technique for testing and estimating causal relations
1216:
1069:
1065:
782:
212:
95:
4783:{\displaystyle CDE(0)=P(Y=1|do(X=1),do(M=0))-P(Y=1|do(X=0),do(M=0))}
2225:{\displaystyle Z\rightarrow X\rightarrow Y\leftarrow U\rightarrow X}
1223:
in a causal model. A causal diagram includes a set of variables (or
6227:
Pearl, Judea; Glymour, Madelyn; Jewell, Nicholas P (7 March 2016).
5985:. In Beebee, Helen; Hitchcock, Christopher; Menzies, Peter (eds.).
5755:(Fall 2018 ed.), Metaphysics Research Lab, Stanford University
4484:{\displaystyle Y\leftarrow X\rightarrow M\rightarrow Y\leftarrow U}
2893:{\displaystyle X\leftarrow A\rightarrow B\leftarrow C\rightarrow Y}
432:
One object is associated with another if observing one changes the
303:
6430:"To Build Truly Intelligent Machines, Teach Them Cause and Effect"
2254:
is an instrumental variable, because it has a path to the outcome
6266:"Deep learning could reveal why the world works the way it does"
4437:
available) a probability-interval statement, such as non-smoker
4296:
The potential outcome is defined at the level of the individual
2795:
Earlier, allegedly incorrect definitions of confounder include:
4945:{\displaystyle NDE=P(Y_{M=M0}=1|do(X=1))-P(Y_{M=M0}=1|do(X=0))}
3700:{\displaystyle P({\text{floss}}\vline do({\text{toothpaste}}))}
2493:
have the same independence conditions, because conditioning on
312:
99:
5140:
The above NDE calculation includes counterfactual subscripts (
5625:
with an explicit requirement that the relationships be causal
624:{\displaystyle P(\mathrm {floss} |do(\mathrm {toothpaste} ))}
238:
in sports) which later led him to the non-causal concept of
5176:). For nonlinear models, the seemingly obvious equivalence
4016:
Rule 3 permits the deletion or addition of interventions.:
71:
3798:
Rule 1 permits the addition or deletion of observations.:
1857:) often reveals a non-causal negative correlation between
283:
that had led Galton to abandon causality, by resurrecting
5513:, whether a study can be applied in a different context.
512:{\displaystyle P(\mathrm {floss} |\mathrm {toothpaste} )}
6384:"AI Algorithms Are Now Shockingly Good at Doing Science"
2792:
X and Y are confounded (by some confounder variable Z).
785:
relied purely on probabilities/associations. One event (
4441:
would have a 10-20% chance of cancer, can be computed.
1695:{\displaystyle A\leftarrow B\rightarrow C\rightarrow A}
761:
not applied to a stationary object, it will not move).
298:
became the theoretical ancestor of causal modeling and
4955:
For example, consider the direct effect of increasing
4585:{\displaystyle Y\leftarrow M\leftarrow X\rightarrow Y}
3543:
3501:
2978:
2812:
The latter is flawed in that given that in the model:
1817:, multiple causes affect one outcome. Conditioning on
420:
expressed as causal relationships. The highest level,
5338:
5185:
5146:
4981:
4806:
4619:
4560:
4453:
4373:
4327:
4262:
4220:
4104:
4025:
3923:
3807:
3656:
3554:
3516:
3465:
3439:
3419:
3399:
3379:
3359:
3339:
3319:
3299:
3273:
3247:
3227:
3178:
3158:
3138:
3112:
3092:
3066:
2989:
2942:
2862:
2821:
2723:
2683:
2663:
2643:
2623:
2599:
2579:
2559:
2539:
2519:
2499:
2464:
2426:
2343:
2323:
2303:
2280:
2260:
2240:
2194:
2131:
2111:
2091:
2071:
2026:
2003:
1983:
1963:
1943:
1923:
1903:
1883:
1863:
1843:
1823:
1791:
1771:
1751:
1731:
1711:
1670:
1644:
1624:
1604:
1569:
1546:
1526:
1506:
1486:
1442:
1419:
1399:
1379:
1313:
1293:
1273:
1253:
1233:
1038:
1018:
936:
910:
890:
834:
811:
791:
657:
545:
445:
164:
6245:
5957:
The Book of Why: The New
Science of Cause and Effect
4793:
Each value of the mediator has a corresponding CDE.
4211:, had X been assigned the value x". Mathematically:
4086:in the case where no causal paths connect X and Y.
3622:{\displaystyle P(Y|do(X))=\textstyle \sum _{z}\left}
2799:"Any variable that is correlated with both X and Y."
5730:
5728:
5726:
5543:Probability of a positive test for a given disease
6226:
5489:
5318:
5168:
5129:
4944:
4782:
4584:
4483:
4420:
4349:
4284:
4248:
4182:
4075:
3993:
3895:
3699:
3621:
3445:
3425:
3405:
3385:
3365:
3345:
3325:
3305:
3285:
3253:
3233:
3213:
3164:
3144:
3124:
3098:
3078:
3044:
2892:
2839:
2781:
2689:
2669:
2649:
2629:
2605:
2585:
2565:
2545:
2525:
2505:
2482:
2444:
2367:
2329:
2309:
2286:
2266:
2246:
2224:
2137:
2117:
2097:
2077:
2044:
2009:
1989:
1969:
1949:
1929:
1909:
1889:
1869:
1849:
1829:
1797:
1777:
1757:
1737:
1717:
1694:
1650:
1630:
1610:
1587:
1552:
1532:
1512:
1492:
1460:
1425:
1405:
1393:is a mediator in that it mediates the change that
1385:
1319:
1299:
1279:
1259:
1239:
1120:would not have occurred but for the occurrence of
1044:
1024:
1000:
916:
896:
872:
817:
797:
749:
623:
511:
188:
2085:is a mediator, because it modifies the effect of
6476:
6459:Learning Representations using Causal Invariance
5723:
2637:implies that observations for a given value of
268:, which became the world leader in statistics.
5950:
5536:outcomes with their associated probabilities.
4431:
3721:
6024:. In Knauff, Markus; Spohn, Wolfgang (eds.).
5130:{\displaystyle NIE=\sum _{m}xxP(Y=1|X=0,M=m)}
3741:needs attention from an expert in Mathematics
2929:the analysis of the causal effect of X on y.
2337:take binary values, then the assumption that
365:Sociologists originally called causal models
6193:
5673:
3671:
1661:An elaboration of a fork is the confounder:
183:
165:
158:defines a causal model as an ordered triple
116:Causal models can help with the question of
6194:Smith, George Davey; Ebrahim, Shah (2008).
3896:{\displaystyle P(Y|do(X),Z,W)=P(Y|do(X),Z)}
2840:{\displaystyle X\rightarrow Z\rightarrow Y}
2802:Y is associated with Z among the unexposed.
2445:{\displaystyle A\rightarrow B\rightarrow C}
1461:{\displaystyle A\rightarrow B\rightarrow C}
1056:Other attempts to define causality include
769:
6328:The International Journal of Biostatistics
4531:=0), modifying the equations accordingly.
3221:. Effectively, there are conditions where
2700:
2483:{\displaystyle A\leftarrow B\rightarrow C}
2411:
2386:
2045:{\displaystyle A\rightarrow B\leftarrow C}
1588:{\displaystyle A\leftarrow B\rightarrow C}
1520:that can be eliminated by conditioning on
6355:
6144:
6115:
5746:
5706:
5696:
5356:
5293:
5245:
5203:
1160:does not require the prior occurrence of
123:Causal models have found applications in
16:Conceptual model in philosophy of science
6427:
6229:Causal Inference in Statistics: A Primer
6215:chapter 3-3 Controlling Confounding Bias
6150:
6109:
2156:
1144:must imply the subsequent occurrence of
825:). Mathematically this is expressed as:
65:
6408:
6067:. Thomson-Brooks/Cole. pp. 25–26.
5997:10.1093/oxfordhb/9780199279739.001.0001
5753:The Stanford Encyclopedia of Philosophy
3669:
3055:
2177:has no direct influence on the outcome.
1032:is the set of background variables and
6477:
6064:Discrete Mathematics with Applications
5980:
5374:
5371:
5368:
5365:
5362:
5359:
5353:
5350:
5347:
5344:
5341:
5311:
5308:
5305:
5302:
5299:
5296:
5290:
5287:
5284:
5281:
5278:
5275:
5272:
5269:
5266:
5263:
5260:
5257:
5254:
5251:
5248:
5242:
5239:
5236:
5233:
5230:
5227:
5224:
5221:
5218:
5215:
5212:
5209:
5206:
5200:
5197:
5194:
5191:
5188:
3755:may be able to help recruit an expert.
3745:needed to understand do-Operator, see
2907:
2174:has no other path to causal variables;
1917:explains away the correlation between
1167:
1001:{\displaystyle P(Y|X,K=k)>P(Y|K=k)}
410:
6324:"An Introduction to Causal Inference"
6321:
6293:
6251:
6210:
6022:"Causal and Counterfactual Inference"
6019:
5946:
5944:
5942:
5940:
5938:
5936:
5934:
5932:
5930:
5928:
5926:
5924:
5922:
5920:
5918:
5916:
5914:
5912:
5910:
5908:
5906:
5904:
5902:
5900:
5898:
5896:
5894:
5892:
5890:
5888:
5886:
5884:
5882:
5880:
5878:
5876:
5874:
5872:
5870:
5868:
5866:
5864:
5862:
5860:
5858:
5856:
5854:
5852:
5850:
5848:
5846:
5844:
5842:
5840:
5838:
5836:
5834:
5832:
5830:
5828:
5826:
5824:
5822:
5820:
5818:
5816:
5814:
5812:
5810:
5808:
5806:
5804:
5802:
5800:
5798:
5796:
5794:
5792:
5790:
5788:
5734:
5598:
3994:{\displaystyle P(Y|do(X),Z)=P(Y|X,Z)}
2782:{\displaystyle P(Y|X)\neq P(Y|do(X))}
189:{\displaystyle \langle U,V,E\rangle }
6381:
6086:
6084:
5786:
5784:
5782:
5780:
5778:
5776:
5774:
5772:
5770:
5768:
4539:Calculate the values of the output (
4202:
4193:
3725:
3353:, there are no unblocked paths from
1360:
1327:(with an associated probability). A
1127:
18:
6263:
6060:
5524:
5521:relevantly different participants.
5503:
4306:
1104:must imply the prior occurrence of
1082:necessary, sufficient, contributory
150:Stanford Encyclopedia of Philosophy
13:
4963:
4519:given the propositional evidence.
4421:{\displaystyle Y_{X}(u)=Y_{Mx}(u)}
4318:states that the potential outcome
4005:
3670:
2657:should show no dependence between
1188:. If the likelihood is 100%, then
740:
737:
734:
731:
728:
714:
711:
708:
705:
702:
699:
696:
693:
690:
687:
677:
674:
671:
668:
665:
642:
611:
608:
605:
602:
599:
596:
593:
590:
587:
584:
565:
562:
559:
556:
553:
502:
499:
496:
493:
490:
487:
484:
481:
478:
475:
465:
462:
459:
456:
453:
14:
6511:
6315:
6081:
5765:
4004:in the case that Z satisfies the
1352:
1200:
781:Twentieth century definitions of
306:, development and environment on
6200:. National Academies Press (US).
5988:The Oxford Handbook of Causation
5954:; Mackenzie, Dana (2018-05-15).
4604:
4543:) using the modified equations.
3730:
3636:
1184:must increase the likelihood of
23:
6450:
6428:Hartnett, Kevin (15 May 2018).
6257:
6220:
6187:
6038:10.7551/mitpress/11252.003.0044
5747:Hitchcock, Christopher (2018),
4076:{\displaystyle P(Y|do(X))=P(Y)}
2406:
1112:, however, does not imply that
530:
6300:. Cambridge University Press.
6130:10.1080/00325481.1979.11715231
6054:
6013:
5974:
5740:
5667:
5484:
5472:
5460:
5442:
5430:
5418:
5403:
5391:
5379:
5124:
5099:
5086:
5074:
5071:
5058:
5045:
5036:
5023:
5010:
5004:
4939:
4936:
4924:
4914:
4885:
4876:
4873:
4861:
4851:
4822:
4777:
4774:
4762:
4750:
4738:
4728:
4715:
4706:
4703:
4691:
4679:
4667:
4657:
4644:
4635:
4629:
4576:
4570:
4564:
4475:
4469:
4463:
4457:
4415:
4409:
4390:
4384:
4344:
4338:
4279:
4273:
4243:
4237:
4177:
4174:
4166:
4156:
4147:
4138:
4135:
4127:
4117:
4108:
4070:
4064:
4055:
4052:
4046:
4036:
4029:
3988:
3975:
3968:
3959:
3950:
3944:
3934:
3927:
3890:
3881:
3875:
3865:
3858:
3849:
3834:
3828:
3818:
3811:
3772:
3694:
3691:
3683:
3660:
3608:
3596:
3590:
3565:
3558:
3540:
3533:
3520:
3495:
3492:
3486:
3476:
3469:
3393:, and all backdoor paths from
3313:intercepts all directed paths
3208:
3205:
3199:
3189:
3182:
3116:
3070:
3037:
3025:
3019:
3000:
2993:
2972:
2969:
2963:
2953:
2946:
2884:
2878:
2872:
2866:
2831:
2825:
2776:
2773:
2767:
2757:
2750:
2741:
2734:
2727:
2474:
2468:
2436:
2430:
2274:and is unconfounded, e.g., by
2216:
2210:
2204:
2198:
2185:For example, given the model:
2036:
2030:
1686:
1680:
1674:
1579:
1573:
1452:
1446:
1176:to be a contributory cause of
995:
982:
975:
966:
947:
940:
873:{\displaystyle P(Y|X)>P(Y)}
867:
861:
852:
845:
838:
744:
682:
661:
618:
615:
580:
570:
549:
506:
470:
449:
427:
1:
6165:10.1016/s0140-6736(86)92972-7
5751:, in Zalta, Edward N. (ed.),
5660:
4089:
2148:
2055:
138:
5981:Okasha, Samir (2012-01-12).
5698:10.1371/journal.pbio.1000033
5629:Structural equation modeling
4546:
3106:where no open paths connect
1136:to be a sufficient cause of
1087:
764:
648:would still have bought it?
367:structural equation modeling
7:
6409:Maudlin, Tim (2019-08-30).
6322:Pearl, Judea (2010-02-26).
6294:Pearl, Judea (2009-09-14).
6026:The Handbook of Rationality
5991:. Vol. 1. OUP Oxford.
5607:
4432:Conducting a counterfactual
3743:. The specific problem is:
3722:Interventional distribution
2060:
1808:
1287:indicates that a change in
1096:to be a necessary cause of
1062:statistical hypothesis test
111:randomized controlled trial
36:to comply with Knowledge's
10:
6516:
6287:
6264:Hao, Karen (May 8, 2019).
5635:Path analysis (statistics)
5528:
4534:
4249:{\displaystyle Y_{X=x}(u)}
3641:
3214:{\displaystyle P(Y|do(X))}
2171:has a path to the outcome;
1638:" (i.e., given a value of
1204:
264:and the Biometrics Lab at
230:introduced the concept of
207:
6231:. John Wiley & Sons.
5549:
4498:
4011:
3909:
3793:
2375:does not occur is called
2297:In the above example, if
1837:(for a specific value of
1540:(for a specific value of
1148:. However, another cause
266:University College London
6382:Falk, Dan (2019-03-17).
6061:Epp, Susanna S. (2004).
5169:{\displaystyle Y_{M=M0}}
4350:{\displaystyle Y_{X}(u)}
4285:{\displaystyle Y_{x}(u)}
3785:
1997:are necessary to affect
1413:would otherwise have on
1368:
1334:Causal diagrams include
1195:
1152:may independently cause
1075:
770:Causality vs correlation
49:may contain suggestions.
34:may need to be rewritten
6500:Concepts in metaphysics
6096:www.istarassessment.org
5650:Dynamic causal modeling
3753:WikiProject Mathematics
3241:can act as a proxy for
2701:Confounder/deconfounder
2412:Independence conditions
2393:Mendelian randomization
2387:Mendelian randomization
2368:{\displaystyle Z=0,X=1}
1471:
1340:directed acyclic graphs
1156:. Thus the presence of
255:correlation coefficient
88:structural causal model
6411:"The Why of the World"
6340:10.2202/1557-4679.1203
5983:"Causation in Biology"
5491:
5320:
5170:
5131:
4946:
4784:
4586:
4522:
4485:
4422:
4351:
4286:
4250:
4184:
4077:
3995:
3897:
3701:
3623:
3447:
3427:
3407:
3387:
3367:
3347:
3327:
3307:
3287:
3286:{\displaystyle z\in Z}
3255:
3235:
3215:
3166:
3146:
3126:
3125:{\displaystyle z\to Y}
3100:
3080:
3079:{\displaystyle X\to Y}
3046:
2894:
2841:
2783:
2691:
2671:
2651:
2631:
2607:
2593:after conditioning on
2587:
2567:
2547:
2527:
2507:
2484:
2446:
2369:
2331:
2311:
2288:
2268:
2248:
2226:
2139:
2119:
2105:(an indirect cause of
2099:
2079:
2046:
2011:
1991:
1971:
1951:
1931:
1911:
1891:
1871:
1851:
1831:
1799:
1779:
1759:
1739:
1719:
1696:
1652:
1632:
1612:
1589:
1554:
1534:
1514:
1494:
1462:
1427:
1407:
1387:
1321:
1301:
1281:
1267:with the arrowhead at
1261:
1241:
1219:relationships between
1211:A causal diagram is a
1046:
1026:
1002:
918:
898:
874:
819:
799:
751:
625:
513:
279:solved the problem of
196:, where U is a set of
190:
153:
75:
6462:, ICLR, February 2020
6270:MIT Technology Review
6118:Postgraduate Medicine
6020:Pearl, Judea (2021).
5492:
5321:
5171:
5132:
4947:
4785:
4587:
4486:
4423:
4352:
4287:
4251:
4185:
4078:
3996:
3898:
3702:
3624:
3448:
3428:
3408:
3388:
3368:
3348:
3328:
3308:
3288:
3256:
3236:
3216:
3167:
3147:
3127:
3101:
3081:
3047:
2895:
2842:
2784:
2692:
2672:
2652:
2632:
2608:
2588:
2568:
2548:
2528:
2508:
2485:
2447:
2397:observational studies
2370:
2332:
2312:
2289:
2269:
2249:
2227:
2164:instrumental variable
2157:Instrumental variable
2140:
2120:
2100:
2080:
2047:
2012:
1992:
1972:
1952:
1932:
1912:
1892:
1872:
1852:
1832:
1800:
1780:
1760:
1740:
1725:is a common cause of
1720:
1697:
1653:
1633:
1613:
1590:
1555:
1535:
1515:
1495:
1463:
1428:
1408:
1388:
1322:
1302:
1282:
1262:
1242:
1205:Further information:
1084:or some combination.
1047:
1027:
1003:
919:
899:
875:
820:
800:
752:
626:
514:
285:Mendelian inheritance
191:
142:
69:
5336:
5183:
5144:
4979:
4804:
4617:
4558:
4451:
4371:
4325:
4260:
4218:
4102:
4023:
3921:
3805:
3654:
3463:
3437:
3417:
3397:
3377:
3357:
3337:
3317:
3297:
3271:
3245:
3225:
3176:
3156:
3136:
3110:
3090:
3064:
3056:Frontdoor adjustment
2940:
2860:
2819:
2721:
2681:
2661:
2641:
2621:
2597:
2577:
2557:
2537:
2517:
2497:
2462:
2424:
2341:
2321:
2301:
2278:
2258:
2238:
2192:
2129:
2109:
2089:
2069:
2024:
2001:
1981:
1961:
1941:
1921:
1901:
1881:
1861:
1841:
1821:
1789:
1769:
1749:
1729:
1709:
1668:
1642:
1622:
1602:
1567:
1544:
1524:
1504:
1484:
1478:spurious correlation
1440:
1417:
1397:
1377:
1336:causal loop diagrams
1311:
1291:
1271:
1251:
1231:
1036:
1016:
934:
908:
888:
832:
809:
789:
655:
543:
443:
321:. One exception was
202:structural equations
162:
5544:
4505:abductive reasoning
4006:back-door criterion
3675:
2908:Backdoor adjustment
1765:(which also causes
1307:causes a change in
1168:Contributory causes
411:Ladder of causation
407:said to be absent.
234:(epitomized by the
198:exogenous variables
102:. Several types of
94:that describes the
6092:"Causal Reasoning"
5655:Rubin causal model
5599:Invariants/context
5542:
5487:
5316:
5166:
5127:
5003:
4942:
4780:
4582:
4481:
4418:
4347:
4282:
4246:
4180:
4073:
3991:
3893:
3697:
3674:
3619:
3618:
3613:
3612:
3611:
3553:
3511:
3443:
3423:
3403:
3383:
3363:
3343:
3323:
3303:
3283:
3251:
3231:
3211:
3162:
3142:
3122:
3096:
3076:
3042:
3041:
3040:
2988:
2890:
2837:
2779:
2687:
2667:
2647:
2627:
2603:
2583:
2563:
2543:
2523:
2503:
2480:
2442:
2365:
2327:
2307:
2284:
2264:
2244:
2222:
2135:
2115:
2095:
2075:
2042:
2007:
1987:
1967:
1947:
1927:
1907:
1887:
1867:
1847:
1827:
1795:
1775:
1755:
1735:
1715:
1692:
1648:
1628:
1608:
1585:
1550:
1530:
1510:
1490:
1458:
1423:
1403:
1383:
1317:
1297:
1277:
1257:
1237:
1180:, the presence of
1140:, the presence of
1108:. The presence of
1100:, the presence of
1042:
1022:
998:
914:
894:
870:
815:
795:
747:
621:
509:
186:
76:
6495:Scientific models
6238:978-1-119-18684-7
5587:
5586:
5511:external validity
5450:
5358:
5295:
5247:
5205:
4994:
4509:logical inference
4444:Given the model:
4314:The first law of
4203:Potential outcome
4172:
4153:
4133:
4132:blood cholesterol
4114:
3770:
3769:
3689:
3666:
3544:
3502:
3446:{\displaystyle X}
3426:{\displaystyle Y}
3406:{\displaystyle Z}
3386:{\displaystyle Y}
3366:{\displaystyle Z}
3346:{\displaystyle Y}
3326:{\displaystyle X}
3306:{\displaystyle Z}
3254:{\displaystyle X}
3234:{\displaystyle Z}
3165:{\displaystyle z}
3152:, the set of all
3145:{\displaystyle Z}
3099:{\displaystyle z}
2979:
2690:{\displaystyle C}
2670:{\displaystyle A}
2650:{\displaystyle B}
2630:{\displaystyle B}
2606:{\displaystyle B}
2586:{\displaystyle C}
2566:{\displaystyle A}
2546:{\displaystyle C}
2526:{\displaystyle A}
2506:{\displaystyle B}
2330:{\displaystyle X}
2310:{\displaystyle Z}
2287:{\displaystyle U}
2267:{\displaystyle Y}
2247:{\displaystyle Z}
2138:{\displaystyle C}
2118:{\displaystyle C}
2098:{\displaystyle A}
2078:{\displaystyle B}
2010:{\displaystyle B}
1990:{\displaystyle C}
1970:{\displaystyle A}
1950:{\displaystyle C}
1930:{\displaystyle A}
1910:{\displaystyle B}
1890:{\displaystyle C}
1870:{\displaystyle A}
1850:{\displaystyle B}
1830:{\displaystyle B}
1798:{\displaystyle B}
1778:{\displaystyle A}
1758:{\displaystyle C}
1738:{\displaystyle A}
1718:{\displaystyle B}
1651:{\displaystyle B}
1631:{\displaystyle B}
1611:{\displaystyle B}
1598:"Conditioning on
1553:{\displaystyle B}
1533:{\displaystyle B}
1513:{\displaystyle C}
1493:{\displaystyle A}
1426:{\displaystyle C}
1406:{\displaystyle A}
1386:{\displaystyle B}
1361:Junction patterns
1344:Ishikawa diagrams
1320:{\displaystyle B}
1300:{\displaystyle A}
1280:{\displaystyle B}
1260:{\displaystyle B}
1240:{\displaystyle A}
1128:Sufficient causes
1058:Granger causality
1045:{\displaystyle k}
1025:{\displaystyle K}
917:{\displaystyle Y}
897:{\displaystyle X}
818:{\displaystyle Y}
798:{\displaystyle X}
125:signal processing
118:external validity
64:
63:
38:quality standards
6507:
6470:
6469:
6468:
6467:
6454:
6443:
6441:
6440:
6424:
6422:
6421:
6405:
6403:
6402:
6369:
6359:
6334:(2): Article 7.
6311:
6281:
6280:
6278:
6276:
6261:
6255:
6249:
6243:
6242:
6224:
6218:
6208:
6202:
6201:
6191:
6185:
6184:
6148:
6142:
6141:
6113:
6107:
6106:
6104:
6102:
6088:
6079:
6078:
6058:
6052:
6051:
6017:
6011:
6010:
5978:
5972:
5971:
5948:
5763:
5762:
5761:
5760:
5744:
5738:
5732:
5721:
5720:
5710:
5700:
5671:
5640:Bayesian network
5623:Bayesian network
5545:
5541:
5531:Bayesian network
5525:Bayesian network
5504:Transportability
5496:
5494:
5493:
5488:
5448:
5378:
5377:
5325:
5323:
5322:
5317:
5315:
5314:
5175:
5173:
5172:
5167:
5165:
5164:
5136:
5134:
5133:
5128:
5102:
5061:
5026:
5002:
4957:dental hygienist
4951:
4949:
4948:
4943:
4917:
4906:
4905:
4854:
4843:
4842:
4789:
4787:
4786:
4781:
4731:
4660:
4591:
4589:
4588:
4583:
4490:
4488:
4487:
4482:
4427:
4425:
4424:
4419:
4408:
4407:
4383:
4382:
4356:
4354:
4353:
4348:
4337:
4336:
4316:causal inference
4307:Causal inference
4291:
4289:
4288:
4283:
4272:
4271:
4255:
4253:
4252:
4247:
4236:
4235:
4189:
4187:
4186:
4181:
4173:
4170:
4159:
4154:
4151:
4134:
4131:
4120:
4115:
4112:
4082:
4080:
4079:
4074:
4039:
4000:
3998:
3997:
3992:
3978:
3937:
3902:
3900:
3899:
3894:
3868:
3821:
3765:
3762:
3756:
3734:
3733:
3726:
3706:
3704:
3703:
3698:
3690:
3687:
3676:
3667:
3664:
3628:
3626:
3625:
3620:
3617:
3568:
3552:
3536:
3510:
3479:
3452:
3450:
3449:
3444:
3432:
3430:
3429:
3424:
3412:
3410:
3409:
3404:
3392:
3390:
3389:
3384:
3372:
3370:
3369:
3364:
3352:
3350:
3349:
3344:
3332:
3330:
3329:
3324:
3312:
3310:
3309:
3304:
3292:
3290:
3289:
3284:
3260:
3258:
3257:
3252:
3240:
3238:
3237:
3232:
3220:
3218:
3217:
3212:
3192:
3171:
3169:
3168:
3163:
3151:
3149:
3148:
3143:
3131:
3129:
3128:
3123:
3105:
3103:
3102:
3097:
3085:
3083:
3082:
3077:
3051:
3049:
3048:
3043:
3003:
2987:
2956:
2913:spurious paths.
2899:
2897:
2896:
2891:
2846:
2844:
2843:
2838:
2788:
2786:
2785:
2780:
2760:
2737:
2696:
2694:
2693:
2688:
2676:
2674:
2673:
2668:
2656:
2654:
2653:
2648:
2636:
2634:
2633:
2628:
2612:
2610:
2609:
2604:
2592:
2590:
2589:
2584:
2572:
2570:
2569:
2564:
2552:
2550:
2549:
2544:
2532:
2530:
2529:
2524:
2512:
2510:
2509:
2504:
2489:
2487:
2486:
2481:
2451:
2449:
2448:
2443:
2374:
2372:
2371:
2366:
2336:
2334:
2333:
2328:
2316:
2314:
2313:
2308:
2293:
2291:
2290:
2285:
2273:
2271:
2270:
2265:
2253:
2251:
2250:
2245:
2231:
2229:
2228:
2223:
2144:
2142:
2141:
2136:
2124:
2122:
2121:
2116:
2104:
2102:
2101:
2096:
2084:
2082:
2081:
2076:
2051:
2049:
2048:
2043:
2016:
2014:
2013:
2008:
1996:
1994:
1993:
1988:
1976:
1974:
1973:
1968:
1956:
1954:
1953:
1948:
1936:
1934:
1933:
1928:
1916:
1914:
1913:
1908:
1896:
1894:
1893:
1888:
1876:
1874:
1873:
1868:
1856:
1854:
1853:
1848:
1836:
1834:
1833:
1828:
1805:the confounder.
1804:
1802:
1801:
1796:
1784:
1782:
1781:
1776:
1764:
1762:
1761:
1756:
1744:
1742:
1741:
1736:
1724:
1722:
1721:
1716:
1705:In such models,
1701:
1699:
1698:
1693:
1657:
1655:
1654:
1649:
1637:
1635:
1634:
1629:
1617:
1615:
1614:
1609:
1594:
1592:
1591:
1586:
1559:
1557:
1556:
1551:
1539:
1537:
1536:
1531:
1519:
1517:
1516:
1511:
1499:
1497:
1496:
1491:
1467:
1465:
1464:
1459:
1432:
1430:
1429:
1424:
1412:
1410:
1409:
1404:
1392:
1390:
1389:
1384:
1326:
1324:
1323:
1318:
1306:
1304:
1303:
1298:
1286:
1284:
1283:
1278:
1266:
1264:
1263:
1258:
1246:
1244:
1243:
1238:
1051:
1049:
1048:
1043:
1031:
1029:
1028:
1023:
1007:
1005:
1004:
999:
985:
950:
923:
921:
920:
915:
903:
901:
900:
895:
879:
877:
876:
871:
848:
824:
822:
821:
816:
804:
802:
801:
796:
756:
754:
753:
748:
743:
717:
685:
680:
630:
628:
627:
622:
614:
573:
568:
518:
516:
515:
510:
505:
473:
468:
195:
193:
192:
187:
151:
133:machine learning
98:mechanisms of a
92:conceptual model
59:
56:
50:
27:
19:
6515:
6514:
6510:
6509:
6508:
6506:
6505:
6504:
6485:Causal diagrams
6475:
6474:
6473:
6465:
6463:
6456:
6455:
6451:
6438:
6436:
6434:Quanta Magazine
6419:
6417:
6400:
6398:
6373:Causal modeling
6318:
6308:
6290:
6285:
6284:
6274:
6272:
6262:
6258:
6250:
6246:
6239:
6225:
6221:
6209:
6205:
6192:
6188:
6159:(8479): 507–8.
6149:
6145:
6114:
6110:
6100:
6098:
6090:
6089:
6082:
6075:
6059:
6055:
6048:
6018:
6014:
6007:
5979:
5975:
5968:
5960:. Basic Books.
5949:
5766:
5758:
5756:
5749:"Causal Models"
5745:
5741:
5733:
5724:
5691:(2): e1000033.
5672:
5668:
5663:
5610:
5601:
5533:
5527:
5506:
5340:
5339:
5337:
5334:
5333:
5187:
5186:
5184:
5181:
5180:
5151:
5147:
5145:
5142:
5141:
5098:
5057:
5022:
4998:
4980:
4977:
4976:
4966:
4964:Indirect effect
4913:
4892:
4888:
4850:
4829:
4825:
4805:
4802:
4801:
4727:
4656:
4618:
4615:
4614:
4607:
4559:
4556:
4555:
4549:
4537:
4525:
4501:
4452:
4449:
4448:
4434:
4400:
4396:
4378:
4374:
4372:
4369:
4368:
4332:
4328:
4326:
4323:
4322:
4309:
4267:
4263:
4261:
4258:
4257:
4225:
4221:
4219:
4216:
4215:
4205:
4196:
4194:Counterfactuals
4169:
4155:
4150:
4130:
4116:
4111:
4103:
4100:
4099:
4092:
4035:
4024:
4021:
4020:
4014:
3974:
3933:
3922:
3919:
3918:
3912:
3864:
3817:
3806:
3803:
3802:
3796:
3788:
3780:polynomial time
3775:
3766:
3760:
3757:
3751:
3735:
3731:
3724:
3686:
3668:
3663:
3655:
3652:
3651:
3644:
3639:
3564:
3548:
3532:
3512:
3506:
3475:
3464:
3461:
3460:
3438:
3435:
3434:
3433:are blocked by
3418:
3415:
3414:
3398:
3395:
3394:
3378:
3375:
3374:
3358:
3355:
3354:
3338:
3335:
3334:
3318:
3315:
3314:
3298:
3295:
3294:
3272:
3269:
3268:
3246:
3243:
3242:
3226:
3223:
3222:
3188:
3177:
3174:
3173:
3172:s, can measure
3157:
3154:
3153:
3137:
3134:
3133:
3111:
3108:
3107:
3091:
3088:
3087:
3065:
3062:
3061:
3058:
2999:
2983:
2952:
2941:
2938:
2937:
2910:
2861:
2858:
2857:
2820:
2817:
2816:
2756:
2733:
2722:
2719:
2718:
2703:
2682:
2679:
2678:
2662:
2659:
2658:
2642:
2639:
2638:
2622:
2619:
2618:
2598:
2595:
2594:
2578:
2575:
2574:
2558:
2555:
2554:
2538:
2535:
2534:
2518:
2515:
2514:
2498:
2495:
2494:
2463:
2460:
2459:
2425:
2422:
2421:
2414:
2409:
2389:
2342:
2339:
2338:
2322:
2319:
2318:
2302:
2299:
2298:
2279:
2276:
2275:
2259:
2256:
2255:
2239:
2236:
2235:
2193:
2190:
2189:
2159:
2151:
2145:(the outcome).
2130:
2127:
2126:
2110:
2107:
2106:
2090:
2087:
2086:
2070:
2067:
2066:
2063:
2058:
2025:
2022:
2021:
2002:
1999:
1998:
1982:
1979:
1978:
1962:
1959:
1958:
1942:
1939:
1938:
1922:
1919:
1918:
1902:
1899:
1898:
1882:
1879:
1878:
1862:
1859:
1858:
1842:
1839:
1838:
1822:
1819:
1818:
1811:
1790:
1787:
1786:
1770:
1767:
1766:
1750:
1747:
1746:
1730:
1727:
1726:
1710:
1707:
1706:
1669:
1666:
1665:
1643:
1640:
1639:
1623:
1620:
1619:
1618:" means "given
1603:
1600:
1599:
1568:
1565:
1564:
1545:
1542:
1541:
1525:
1522:
1521:
1505:
1502:
1501:
1485:
1482:
1481:
1474:
1441:
1438:
1437:
1418:
1415:
1414:
1398:
1395:
1394:
1378:
1375:
1374:
1371:
1363:
1355:
1312:
1309:
1308:
1292:
1289:
1288:
1272:
1269:
1268:
1252:
1249:
1248:
1232:
1229:
1228:
1209:
1203:
1198:
1170:
1130:
1090:
1080:A cause can be
1078:
1037:
1034:
1033:
1017:
1014:
1013:
981:
946:
935:
932:
931:
909:
906:
905:
889:
886:
885:
844:
833:
830:
829:
810:
807:
806:
790:
787:
786:
772:
767:
727:
686:
681:
664:
656:
653:
652:
645:
643:Counterfactuals
583:
569:
552:
544:
541:
540:
533:
474:
469:
452:
444:
441:
440:
430:
422:Counterfactuals
415:Pearl's causal
413:
281:trait stability
236:sophomore slump
232:mean regression
217:counterfactuals
210:
163:
160:
159:
152:
149:
141:
104:causal notation
60:
54:
51:
41:
28:
17:
12:
11:
5:
6513:
6503:
6502:
6497:
6492:
6487:
6472:
6471:
6448:
6447:
6446:
6444:
6425:
6406:
6379:
6370:
6317:
6316:External links
6314:
6313:
6312:
6306:
6289:
6286:
6283:
6282:
6256:
6254:, p. 207.
6244:
6237:
6219:
6203:
6186:
6143:
6124:(2): 177–179.
6108:
6080:
6073:
6053:
6046:
6012:
6005:
5973:
5966:
5764:
5739:
5722:
5665:
5664:
5662:
5659:
5658:
5657:
5652:
5647:
5642:
5637:
5632:
5626:
5619:Causal network
5616:
5609:
5606:
5600:
5597:
5585:
5584:
5581:
5578:
5574:
5573:
5570:
5567:
5563:
5562:
5559:
5556:
5552:
5551:
5548:
5529:Main article:
5526:
5523:
5505:
5502:
5498:
5497:
5486:
5483:
5480:
5477:
5474:
5471:
5468:
5465:
5462:
5459:
5456:
5453:
5447:
5444:
5441:
5438:
5435:
5432:
5429:
5426:
5423:
5420:
5417:
5414:
5411:
5408:
5405:
5402:
5399:
5396:
5393:
5390:
5387:
5384:
5381:
5376:
5373:
5370:
5367:
5364:
5361:
5355:
5352:
5349:
5346:
5343:
5327:
5326:
5313:
5310:
5307:
5304:
5301:
5298:
5292:
5289:
5286:
5283:
5280:
5277:
5274:
5271:
5268:
5265:
5262:
5259:
5256:
5253:
5250:
5244:
5241:
5238:
5235:
5232:
5229:
5226:
5223:
5220:
5217:
5214:
5211:
5208:
5202:
5199:
5196:
5193:
5190:
5163:
5160:
5157:
5154:
5150:
5138:
5137:
5126:
5123:
5120:
5117:
5114:
5111:
5108:
5105:
5101:
5097:
5094:
5091:
5088:
5085:
5082:
5079:
5076:
5073:
5070:
5067:
5064:
5060:
5056:
5053:
5050:
5047:
5044:
5041:
5038:
5035:
5032:
5029:
5025:
5021:
5018:
5015:
5012:
5009:
5006:
5001:
4997:
4993:
4990:
4987:
4984:
4965:
4962:
4953:
4952:
4941:
4938:
4935:
4932:
4929:
4926:
4923:
4920:
4916:
4912:
4909:
4904:
4901:
4898:
4895:
4891:
4887:
4884:
4881:
4878:
4875:
4872:
4869:
4866:
4863:
4860:
4857:
4853:
4849:
4846:
4841:
4838:
4835:
4832:
4828:
4824:
4821:
4818:
4815:
4812:
4809:
4791:
4790:
4779:
4776:
4773:
4770:
4767:
4764:
4761:
4758:
4755:
4752:
4749:
4746:
4743:
4740:
4737:
4734:
4730:
4726:
4723:
4720:
4717:
4714:
4711:
4708:
4705:
4702:
4699:
4696:
4693:
4690:
4687:
4684:
4681:
4678:
4675:
4672:
4669:
4666:
4663:
4659:
4655:
4652:
4649:
4646:
4643:
4640:
4637:
4634:
4631:
4628:
4625:
4622:
4606:
4603:
4581:
4578:
4575:
4572:
4569:
4566:
4563:
4548:
4545:
4536:
4533:
4524:
4521:
4500:
4497:
4492:
4491:
4480:
4477:
4474:
4471:
4468:
4465:
4462:
4459:
4456:
4433:
4430:
4429:
4428:
4417:
4414:
4411:
4406:
4403:
4399:
4395:
4392:
4389:
4386:
4381:
4377:
4358:
4357:
4346:
4343:
4340:
4335:
4331:
4308:
4305:
4294:
4293:
4281:
4278:
4275:
4270:
4266:
4245:
4242:
4239:
4234:
4231:
4228:
4224:
4204:
4201:
4195:
4192:
4191:
4190:
4179:
4176:
4168:
4165:
4162:
4158:
4149:
4146:
4143:
4140:
4137:
4129:
4126:
4123:
4119:
4110:
4107:
4091:
4088:
4084:
4083:
4072:
4069:
4066:
4063:
4060:
4057:
4054:
4051:
4048:
4045:
4042:
4038:
4034:
4031:
4028:
4013:
4010:
4002:
4001:
3990:
3987:
3984:
3981:
3977:
3973:
3970:
3967:
3964:
3961:
3958:
3955:
3952:
3949:
3946:
3943:
3940:
3936:
3932:
3929:
3926:
3911:
3908:
3904:
3903:
3892:
3889:
3886:
3883:
3880:
3877:
3874:
3871:
3867:
3863:
3860:
3857:
3854:
3851:
3848:
3845:
3842:
3839:
3836:
3833:
3830:
3827:
3824:
3820:
3816:
3813:
3810:
3795:
3792:
3787:
3784:
3774:
3771:
3768:
3767:
3738:
3736:
3729:
3723:
3720:
3708:
3707:
3696:
3693:
3685:
3682:
3679:
3673:
3662:
3659:
3643:
3640:
3638:
3635:
3630:
3629:
3616:
3610:
3607:
3604:
3601:
3598:
3595:
3592:
3589:
3586:
3583:
3580:
3577:
3574:
3571:
3567:
3563:
3560:
3557:
3551:
3547:
3542:
3539:
3535:
3531:
3528:
3525:
3522:
3519:
3515:
3509:
3505:
3500:
3497:
3494:
3491:
3488:
3485:
3482:
3478:
3474:
3471:
3468:
3442:
3422:
3402:
3382:
3362:
3342:
3322:
3302:
3282:
3279:
3276:
3250:
3230:
3210:
3207:
3204:
3201:
3198:
3195:
3191:
3187:
3184:
3181:
3161:
3141:
3121:
3118:
3115:
3095:
3086:have elements
3075:
3072:
3069:
3057:
3054:
3053:
3052:
3039:
3036:
3033:
3030:
3027:
3024:
3021:
3018:
3015:
3012:
3009:
3006:
3002:
2998:
2995:
2992:
2986:
2982:
2977:
2974:
2971:
2968:
2965:
2962:
2959:
2955:
2951:
2948:
2945:
2909:
2906:
2901:
2900:
2889:
2886:
2883:
2880:
2877:
2874:
2871:
2868:
2865:
2848:
2847:
2836:
2833:
2830:
2827:
2824:
2810:
2809:
2806:
2803:
2800:
2790:
2789:
2778:
2775:
2772:
2769:
2766:
2763:
2759:
2755:
2752:
2749:
2746:
2743:
2740:
2736:
2732:
2729:
2726:
2702:
2699:
2686:
2666:
2646:
2626:
2602:
2582:
2562:
2542:
2522:
2502:
2491:
2490:
2479:
2476:
2473:
2470:
2467:
2453:
2452:
2441:
2438:
2435:
2432:
2429:
2413:
2410:
2408:
2405:
2388:
2385:
2364:
2361:
2358:
2355:
2352:
2349:
2346:
2326:
2306:
2283:
2263:
2243:
2233:
2232:
2221:
2218:
2215:
2212:
2209:
2206:
2203:
2200:
2197:
2179:
2178:
2175:
2172:
2158:
2155:
2150:
2147:
2134:
2114:
2094:
2074:
2062:
2059:
2057:
2054:
2053:
2052:
2041:
2038:
2035:
2032:
2029:
2006:
1986:
1966:
1946:
1926:
1906:
1886:
1866:
1846:
1826:
1810:
1807:
1794:
1774:
1754:
1734:
1714:
1703:
1702:
1691:
1688:
1685:
1682:
1679:
1676:
1673:
1647:
1627:
1607:
1596:
1595:
1584:
1581:
1578:
1575:
1572:
1549:
1529:
1509:
1489:
1473:
1470:
1469:
1468:
1457:
1454:
1451:
1448:
1445:
1422:
1402:
1382:
1370:
1367:
1362:
1359:
1354:
1353:Model elements
1351:
1316:
1296:
1276:
1256:
1236:
1215:that displays
1213:directed graph
1202:
1201:Causal diagram
1199:
1197:
1194:
1169:
1166:
1129:
1126:
1089:
1086:
1077:
1074:
1041:
1021:
1010:
1009:
997:
994:
991:
988:
984:
980:
977:
974:
971:
968:
965:
962:
959:
956:
953:
949:
945:
942:
939:
913:
893:
882:
881:
869:
866:
863:
860:
857:
854:
851:
847:
843:
840:
837:
814:
794:
771:
768:
766:
763:
758:
757:
746:
742:
739:
736:
733:
730:
726:
723:
720:
716:
713:
710:
707:
704:
701:
698:
695:
692:
689:
684:
679:
676:
673:
670:
667:
663:
660:
644:
641:
632:
631:
620:
617:
613:
610:
607:
604:
601:
598:
595:
592:
589:
586:
582:
579:
576:
572:
567:
564:
561:
558:
555:
551:
548:
532:
529:
520:
519:
508:
504:
501:
498:
495:
492:
489:
486:
483:
480:
477:
472:
467:
464:
461:
458:
455:
451:
448:
429:
426:
412:
409:
346:In the 1960s,
223:" causation).
209:
206:
185:
182:
179:
176:
173:
170:
167:
147:
140:
137:
62:
61:
31:
29:
22:
15:
9:
6:
4:
3:
2:
6512:
6501:
6498:
6496:
6493:
6491:
6488:
6486:
6483:
6482:
6480:
6461:
6460:
6453:
6449:
6445:
6435:
6431:
6426:
6416:
6415:Boston Review
6412:
6407:
6397:
6393:
6389:
6385:
6380:
6378:
6374:
6371:
6367:
6363:
6358:
6353:
6349:
6345:
6341:
6337:
6333:
6329:
6325:
6320:
6319:
6309:
6307:9781139643986
6303:
6299:
6298:
6292:
6291:
6271:
6267:
6260:
6253:
6248:
6240:
6234:
6230:
6223:
6216:
6212:
6207:
6199:
6198:
6190:
6182:
6178:
6174:
6170:
6166:
6162:
6158:
6154:
6147:
6139:
6135:
6131:
6127:
6123:
6119:
6112:
6097:
6093:
6087:
6085:
6076:
6074:9780534359454
6070:
6066:
6065:
6057:
6049:
6047:9780262366175
6043:
6039:
6035:
6031:
6027:
6023:
6016:
6008:
6006:9780191629464
6002:
5998:
5994:
5990:
5989:
5984:
5977:
5969:
5967:9780465097616
5963:
5959:
5958:
5953:
5947:
5945:
5943:
5941:
5939:
5937:
5935:
5933:
5931:
5929:
5927:
5925:
5923:
5921:
5919:
5917:
5915:
5913:
5911:
5909:
5907:
5905:
5903:
5901:
5899:
5897:
5895:
5893:
5891:
5889:
5887:
5885:
5883:
5881:
5879:
5877:
5875:
5873:
5871:
5869:
5867:
5865:
5863:
5861:
5859:
5857:
5855:
5853:
5851:
5849:
5847:
5845:
5843:
5841:
5839:
5837:
5835:
5833:
5831:
5829:
5827:
5825:
5823:
5821:
5819:
5817:
5815:
5813:
5811:
5809:
5807:
5805:
5803:
5801:
5799:
5797:
5795:
5793:
5791:
5789:
5787:
5785:
5783:
5781:
5779:
5777:
5775:
5773:
5771:
5769:
5754:
5750:
5743:
5736:
5731:
5729:
5727:
5718:
5714:
5709:
5704:
5699:
5694:
5690:
5686:
5685:
5680:
5676:
5670:
5666:
5656:
5653:
5651:
5648:
5646:
5643:
5641:
5638:
5636:
5633:
5630:
5627:
5624:
5620:
5617:
5615:
5614:Causal system
5612:
5611:
5605:
5596:
5593:
5590:
5582:
5579:
5576:
5575:
5571:
5568:
5565:
5564:
5560:
5557:
5554:
5553:
5547:
5546:
5540:
5537:
5532:
5522:
5518:
5514:
5512:
5501:
5481:
5478:
5475:
5469:
5466:
5463:
5457:
5454:
5451:
5445:
5439:
5436:
5433:
5427:
5424:
5421:
5415:
5412:
5409:
5406:
5400:
5397:
5394:
5388:
5385:
5382:
5332:
5331:
5330:
5179:
5178:
5177:
5161:
5158:
5155:
5152:
5148:
5121:
5118:
5115:
5112:
5109:
5106:
5103:
5095:
5092:
5089:
5083:
5080:
5077:
5068:
5065:
5062:
5054:
5051:
5048:
5042:
5039:
5033:
5030:
5027:
5019:
5016:
5013:
5007:
4999:
4995:
4991:
4988:
4985:
4982:
4975:
4974:
4973:
4969:
4961:
4958:
4933:
4930:
4927:
4921:
4918:
4910:
4907:
4902:
4899:
4896:
4893:
4889:
4882:
4879:
4870:
4867:
4864:
4858:
4855:
4847:
4844:
4839:
4836:
4833:
4830:
4826:
4819:
4816:
4813:
4810:
4807:
4800:
4799:
4798:
4794:
4771:
4768:
4765:
4759:
4756:
4753:
4747:
4744:
4741:
4735:
4732:
4724:
4721:
4718:
4712:
4709:
4700:
4697:
4694:
4688:
4685:
4682:
4676:
4673:
4670:
4664:
4661:
4653:
4650:
4647:
4641:
4638:
4632:
4626:
4623:
4620:
4613:
4612:
4611:
4605:Direct effect
4602:
4598:
4595:
4592:
4579:
4573:
4567:
4561:
4553:
4544:
4542:
4532:
4530:
4520:
4518:
4514:
4510:
4506:
4496:
4478:
4472:
4466:
4460:
4454:
4447:
4446:
4445:
4442:
4440:
4412:
4404:
4401:
4397:
4393:
4387:
4379:
4375:
4367:
4366:
4365:
4363:
4341:
4333:
4329:
4321:
4320:
4319:
4317:
4312:
4304:
4300:
4299:
4276:
4268:
4264:
4240:
4232:
4229:
4226:
4222:
4214:
4213:
4212:
4210:
4200:
4163:
4160:
4152:Heart disease
4144:
4141:
4124:
4121:
4113:Heart disease
4105:
4098:
4097:
4096:
4087:
4067:
4061:
4058:
4049:
4043:
4040:
4032:
4026:
4019:
4018:
4017:
4009:
4007:
3985:
3982:
3979:
3971:
3965:
3962:
3956:
3953:
3947:
3941:
3938:
3930:
3924:
3917:
3916:
3915:
3907:
3887:
3884:
3878:
3872:
3869:
3861:
3855:
3852:
3846:
3843:
3840:
3837:
3831:
3825:
3822:
3814:
3808:
3801:
3800:
3799:
3791:
3783:
3781:
3764:
3754:
3750:
3748:
3742:
3739:This article
3737:
3728:
3727:
3719:
3716:
3713:
3680:
3677:
3657:
3650:
3649:
3648:
3637:Interventions
3634:
3614:
3605:
3602:
3599:
3593:
3587:
3584:
3581:
3578:
3575:
3572:
3569:
3561:
3555:
3549:
3545:
3537:
3529:
3526:
3523:
3517:
3513:
3507:
3503:
3498:
3489:
3483:
3480:
3472:
3466:
3459:
3458:
3457:
3454:
3440:
3420:
3400:
3380:
3360:
3340:
3320:
3300:
3280:
3277:
3274:
3266:
3262:
3248:
3228:
3202:
3196:
3193:
3185:
3179:
3159:
3139:
3119:
3113:
3093:
3073:
3067:
3034:
3031:
3028:
3022:
3016:
3013:
3010:
3007:
3004:
2996:
2990:
2984:
2980:
2975:
2966:
2960:
2957:
2949:
2943:
2936:
2935:
2934:
2930:
2926:
2924:
2920:
2918:
2914:
2905:
2887:
2881:
2875:
2869:
2863:
2856:
2855:
2854:
2853:In the model
2851:
2834:
2828:
2822:
2815:
2814:
2813:
2807:
2804:
2801:
2798:
2797:
2796:
2793:
2770:
2764:
2761:
2753:
2747:
2744:
2738:
2730:
2724:
2717:
2716:
2715:
2711:
2709:
2698:
2684:
2664:
2644:
2624:
2614:
2600:
2580:
2560:
2540:
2520:
2500:
2477:
2471:
2465:
2458:
2457:
2456:
2439:
2433:
2427:
2420:
2419:
2418:
2404:
2400:
2398:
2394:
2384:
2380:
2378:
2362:
2359:
2356:
2353:
2350:
2347:
2344:
2324:
2304:
2295:
2281:
2261:
2241:
2219:
2213:
2207:
2201:
2195:
2188:
2187:
2186:
2183:
2176:
2173:
2170:
2169:
2168:
2167:is one that:
2166:
2165:
2154:
2146:
2132:
2112:
2092:
2072:
2039:
2033:
2027:
2020:
2019:
2018:
2004:
1984:
1964:
1944:
1924:
1904:
1884:
1864:
1844:
1824:
1816:
1806:
1792:
1772:
1752:
1732:
1712:
1689:
1683:
1677:
1671:
1664:
1663:
1662:
1659:
1645:
1625:
1605:
1582:
1576:
1570:
1563:
1562:
1561:
1547:
1527:
1507:
1487:
1479:
1455:
1449:
1443:
1436:
1435:
1434:
1420:
1400:
1380:
1366:
1358:
1350:
1347:
1345:
1341:
1337:
1332:
1330:
1314:
1294:
1274:
1254:
1234:
1226:
1222:
1218:
1214:
1208:
1193:
1191:
1187:
1183:
1179:
1175:
1165:
1163:
1159:
1155:
1151:
1147:
1143:
1139:
1135:
1125:
1123:
1119:
1115:
1111:
1107:
1103:
1099:
1095:
1085:
1083:
1073:
1071:
1067:
1063:
1059:
1054:
1039:
1019:
992:
989:
986:
978:
972:
969:
963:
960:
957:
954:
951:
943:
937:
930:
929:
928:
925:
911:
891:
864:
858:
855:
849:
841:
835:
828:
827:
826:
812:
792:
784:
779:
777:
762:
724:
721:
718:
658:
651:
650:
649:
640:
637:
577:
574:
546:
539:
538:
537:
528:
525:
446:
439:
438:
437:
435:
425:
423:
418:
408:
405:
401:
396:
394:
389:
387:
382:
377:
375:
370:
368:
363:
361:
357:
353:
349:
344:
342:
337:
335:
330:
328:
324:
320:
315:
314:
309:
305:
301:
300:causal graphs
297:
296:path analysis
293:
288:
286:
282:
278:
274:
269:
267:
263:
262:
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5682:
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5675:Karl Friston
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2401:
2391:Definition:
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84:causal model
83:
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43:You can help
33:
3773:Do calculus
524:correlation
434:probability
428:Association
240:correlation
156:Judea Pearl
80:metaphysics
6479:Categories
6466:2020-02-10
6439:2019-09-19
6420:2019-09-09
6401:2019-03-20
6377:PhilPapers
6252:Pearl 2009
6211:Pearl 2009
5759:2018-09-08
5735:Pearl 2009
5661:References
5645:Causal map
4090:Extensions
3710:where the
3688:toothpaste
3265:Definition
2923:Definition
2917:Definition
2149:Confounder
2056:Node types
1785:), making
393:Cartwright
356:Goldberger
308:guinea pig
261:Biometrika
247:positivist
139:Definition
55:March 2020
6490:Causality
6396:1059-1028
6348:1557-4679
6297:Causality
6030:MIT Press
5577:Positive
5566:Negative
5561:Negative
5558:Positive
5473:→
5446:−
5431:→
5392:→
5040:−
4996:∑
4880:−
4710:−
4577:→
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4565:←
4547:Mediation
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3504:∑
3278:∈
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1815:colliders
1687:→
1681:→
1675:←
1580:→
1574:←
1453:→
1447:→
1221:variables
1088:Necessary
1070:economics
1066:causality
783:causality
765:Causality
725:∗
417:metamodel
400:Greenland
332:In 1923,
213:Aristotle
184:⟩
166:⟨
47:talk page
6366:20305706
6181:38327985
5717:19226186
5608:See also
5555:Disease
3761:May 2024
2708:a priori
2061:Mediator
1809:Collider
1480:between
391:In 1983
379:In 1973
339:In 1958
327:mediator
313:in utero
304:heredity
290:In 1921
277:Weinberg
271:In 1908
148:—
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6288:Sources
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6101:2 March
5708:2642881
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352:Blalock
251:Pearson
221:but-for
208:History
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3794:Rule 1
1342:, and
1217:causal
1012:where
634:where
404:Robins
374:Karlin
360:Ogburn
348:Duncan
334:Neyman
319:Fisher
292:Wright
228:Galton
100:system
96:causal
74:images
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6388:Wired
6177:S2CID
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2125:) on
1369:Chain
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1196:Model
1076:Types
1064:that
386:Rubin
381:Lewis
323:Burks
273:Hardy
245:As a
6392:ISSN
6362:PMID
6344:ISSN
6302:ISBN
6277:2020
6233:ISBN
6169:PMID
6134:PMID
6103:2016
6069:ISBN
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5962:ISBN
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5621:– a
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