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Causality refers to the mutual influence between events. Causality differs from correlation because B occurs only when A occurs, and if A does not occur, B will not occur. Only by intervening in event A and then examining the result of B can one determine whether there is a causal relationship between A and B.

Causality refers to the mutual influence between events. Causality differs from correlation because B occurs only when A occurs, and if A does not occur, B will not occur. Only by intervening in event A and then examining the result of B can one determine whether there is a causal relationship between A and B.

With the further development of [[causal inference]] in recent years, it is now possible to use a mathematical framework to quantify causality. [[Causality]] describes the [[causal effect]] of a dynamical process <ref name=":14">Pearl J. Causality[M]. Cambridge university press, 2009.</ref><ref>Granger C W. Investigating causal relations by econometric models and cross-spectral methods[J]. Econometrica: journal of the Econometric Society, 1969, 424-438.</ref><ref name=":8">Pearl J. Models, reasoning and inference[J]. Cambridge, UK: CambridgeUniversityPress, 2000, 19(2).</ref>. Judea Pearl <ref name=":8" /> uses [[probabilistic graphical models]] to describe causal interactions. Pearl uses different models to distinguish and quantify three layers of causality. Here we are more concerned with the second layer in the [[causal ladder]]: [[intervening]] in the input distribution. Quantifying the causal effect between two variables is challenging due to inherent uncertainty and ambiguity. Many independent historical studies have addressed the issue of measuring causal relationships. These measurement methods include [[Hume]]'s [[concept of constant connection]] <ref>Spirtes, P.; Glymour, C.; Scheines, R. Causation Prediction and Search, 2nd ed.; MIT Press: Cambridge, MA, USA, 2000.</ref> and value function-based methods <ref>Chickering, D.M. Learning equivalence classes of Bayesian-network structures. J. Mach. Learn. Res. 2002, 2, 445–498.</ref>, Eells and Suppes' probabilistic measures of causation <ref>Eells, E. Probabilistic Causality; Cambridge University Press: Cambridge, UK, 1991; Volume 1</ref><ref>Suppes, P. A probabilistic theory of causality. Br. J. Philos. Sci. 1973, 24, 409–410.</ref>, and Judea Pearl's [[measures of causation]] indicators among others. <ref name=":14" />.

With the further development of [[causal inference]] in recent years, it is now possible to use a mathematical framework to quantify causality. [[Causality]] here describes the [[causal effect]] of a dynamical process or a causal mechanism <ref name=":14">Pearl J. Causality[M]. Cambridge university press, 2009.</ref><ref>Granger C W. Investigating causal relations by econometric models and cross-spectral methods[J]. Econometrica: journal of the Econometric Society, 1969, 424-438.</ref><ref name=":8">Pearl J. Models, reasoning and inference[J]. Cambridge, UK: CambridgeUniversityPress, 2000, 19(2).</ref>. Judea Pearl <ref name=":8" /> uses [[probabilistic graphical models]] to describe causal interactions. Pearl uses different models to distinguish and quantify three layers of causality. Here we are more concerned with the second layer in the [[causal ladder]]: [[intervening]] in the input distribution. Quantifying the causal effect between two variables is challenging due to inherent uncertainty and ambiguity. Many independent historical studies have addressed the issue of measuring causal relationships. These measurement methods include [[Hume]]'s [[concept of constant connection]] <ref>Spirtes, P.; Glymour, C.; Scheines, R. Causation Prediction and Search, 2nd ed.; MIT Press: Cambridge, MA, USA, 2000.</ref> and value function-based methods <ref>Chickering, D.M. Learning equivalence classes of Bayesian-network structures. J. Mach. Learn. Res. 2002, 2, 445–498.</ref>, Eells and Suppes' probabilistic measures of causation <ref>Eells, E. Probabilistic Causality; Cambridge University Press: Cambridge, UK, 1991; Volume 1</ref><ref>Suppes, P. A probabilistic theory of causality. Br. J. Philos. Sci. 1973, 24, 409–410.</ref>, and Judea Pearl's [[measures of causation]] indicators among others. <ref name=":14" />.

==== Causal emergence ====

==== Causal emergence ====