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Causal node

Variable represented in a causal graph that can influence or be influenced by other variables through directed arcs. Each node corresponds to an entity or concept in the studied system.

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Causal arc

Directed arrow connecting two nodes in a DAG representing a direct cause-and-effect relationship between the corresponding variables. The orientation of the arc indicates the direction of causal influence.

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Causal structure

Global configuration of nodes and arcs in a causal graph that captures the complete set of causal relationships in the system. The structure determines the conditional independence constraints observable in the data.

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d-separation criterion

Graphical test allowing to determine whether two sets of variables are conditionally independent given a third set in a DAG. d-separation is crucial for identifying causal effects that can be identified from observational data.

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Structural equations

System of mathematical equations describing how each variable is generated from its direct causes and independent error terms. Structural equations provide a quantitative model of causal mechanisms.

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SCM (Structural Causal Model)

Formal framework combining a causal graph, structural equations, and a distribution over exogenous variables to completely model a causal system. SCMs enable the simulation of interventions and counterfactuals.

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Collider

Structure in a DAG where two arrows converge on the same node, indicating that this node is causally influenced by two distinct variables. Colliders create conditional dependencies when controlled for.

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Causal chain

Sequence of variables where each directly influences the next, forming a continuous causal path in the DAG. Causal chains are essential for understanding mediation mechanisms.

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Fork

Causal structure where a common variable influences two other variables, creating a statistical association between them. Forks represent classic sources of confounding in causal analysis.

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Causal ancestor

Variable that can reach another variable by following directed arcs in a DAG, representing a direct or indirect cause. Ancestors are crucial for identifying potential confounding paths.

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Causal descendant

Variable accessible from another variable by following directed arcs in a DAG, representing a direct or indirect effect. Descendants must be avoided as adjustment variables to prevent introducing bias.

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Moral graph

Transformation of a DAG where unconnected parents of the same node are linked and all arrows are replaced by undirected edges. The moral graph is used for inference in Bayesian networks.

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Pearl's causality

Formal theory of causality based on DAGs and do-calculus, developed by Judea Pearl to unify causal inference. This approach hierarchizes knowledge from association to intervention and then to counterfactual.

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