Causality detection: Difference between revisions
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== Definition of causality == | == Definition of causality == | ||
To start with, it is not even easy to ''define'' what causality means exactly. <ref>[[Wikipedia:Causality]]</ref><ref>[[Wikipedia:Causality_(physics)]]</ref> In philosophy, causality typically refers to a relation between two events X and Y such that: | To start with, it is not even easy to ''define'' what causality means exactly. <ref>[[Wikipedia:Causality|Causality]]</ref><ref>[[Wikipedia:Causality_(physics)|Causality_(physics)]]</ref> In philosophy, causality typically refers to a relation between two events X and Y such that: | ||
* if Y occurs, then X will occur; or | * if Y occurs, then X will occur; or | ||
* if X occurs, then Y must have occured. | * if X occurs, then Y must have occured. | ||
Thus, causality typically involves at least a temporal ''delay'' between the two events. | Thus, causality typically involves at least a temporal ''delay'' between the two events. | ||
In the context of data analysis, it is more productive to adopt [[Wikipedia:Norbert_Wiener|Wiener]]'s 'quantifiable causality'. <ref>N. Wiener. ''The theory of prediction.'' Modern Mathematics for Engineers, Mc-Graw Hill, New York, 1956, ISBN 0486497461</ref> It states: | In the context of data analysis, it is more productive to adopt [[Wikipedia:Norbert_Wiener|Wiener]]'s 'quantifiable causality'. <ref>N. Wiener. ''The theory of prediction.'' Modern Mathematics for Engineers, Mc-Graw Hill, New York, 1956, {{ISBN|0486497461}}</ref> It states: | ||
* if we can predict X better by using the past information from Y than without it, then we call Y causal to X. | * if we can predict X better by using the past information from Y than without it, then we call Y causal to X. | ||
== Traditional approaches == | |||
Traditional approaches to the determination of causal relationships between various (fluctuating) variables include a wide range of methods. | |||
* If intervention in the system is possible, one may control (modulate) one variable and observe the (delayed) effect on other variables. | |||
* Observe systematic time delays between characteristic events or observe systematic precursors to characteristic events. | |||
* Predict the system evolution from a (numerical) model. If successful, the model equations may reveal causal relations. | |||
* Quantify parameters related to system evolution (growth rates, damping rates). | |||
* Use techniques such as correlations, conditional averages; these linear analysis techniques by themselves cannot reveal causality, but additional reasoning (based on physical insight or models) may allow drawing conclusions. | |||
In the fusion context, see <ref>K.H. Burrell, ''Tests of causality: Experimental evidence that sheared <math>E \times B</math> flow alters turbulence and transport in tokamaks'', [[doi:10.1063/1.873728|Phys. Plasmas, '''6'''(12):4418, 1999]]</ref>. | |||
== Analysis techniques == | == Analysis techniques == | ||
Several techniques have been elaborated to quantify | Several techniques have been elaborated to quantify Wiener's causality on the basis of measured time series. | ||
<ref>K. Hlaváková-Schindler, M. Palus, M. Vejmelka, and J. Bhattacharya. ''Causality detection based on information-theoretic approaches in time series analysis'', [[doi:10.1016/j.physrep.2006.12.004|Phys. Reports, '''441'''(1):1, 2007]]</ref> | <ref>K. Hlaváková-Schindler, M. Palus, M. Vejmelka, and J. Bhattacharya. ''Causality detection based on information-theoretic approaches in time series analysis'', [[doi:10.1016/j.physrep.2006.12.004|Phys. Reports, '''441'''(1):1, 2007]]</ref> | ||
Recently, a specific technique taken from Information Theory (the | Recently, a specific technique taken from Information Theory (the [[:Wikipedia:Transfer entropy|Transfer Entropy]])<ref>T. Schreiber, ''Measuring information transfer'', [[doi:10.1103/PhysRevLett.85.461|Phys. Rev. Lett., '''85'''(2):461, 2000]]</ref> was applied succesfully to fluctuation data from fusion devices. | ||
<ref>B.Ph. van Milligen, G. Birkenmeier, M. Ramisch, T. Estrada, C. Hidalgo, and A. Alonso, ''Causality detection and turbulence in fusion plasmas'', [[doi:10.1088/0029-5515/54/2/023011|Nucl. Fusion 54 (2014), 023011]]</ref> | <ref>B.Ph. van Milligen, G. Birkenmeier, M. Ramisch, T. Estrada, C. Hidalgo, and A. Alonso, ''Causality detection and turbulence in fusion plasmas'', [[doi:10.1088/0029-5515/54/2/023011|Nucl. Fusion 54 (2014), 023011]]</ref> | ||
== References == | == References == | ||
<references /> | <references /> | ||
Latest revision as of 11:40, 26 January 2023
The determination of a causal interaction between fluctuating variables in a complex system, such as a fusion-grade plasma, is not straightforward.
Definition of causality
To start with, it is not even easy to define what causality means exactly. [1][2] In philosophy, causality typically refers to a relation between two events X and Y such that:
- if Y occurs, then X will occur; or
- if X occurs, then Y must have occured.
Thus, causality typically involves at least a temporal delay between the two events.
In the context of data analysis, it is more productive to adopt Wiener's 'quantifiable causality'. [3] It states:
- if we can predict X better by using the past information from Y than without it, then we call Y causal to X.
Traditional approaches
Traditional approaches to the determination of causal relationships between various (fluctuating) variables include a wide range of methods.
- If intervention in the system is possible, one may control (modulate) one variable and observe the (delayed) effect on other variables.
- Observe systematic time delays between characteristic events or observe systematic precursors to characteristic events.
- Predict the system evolution from a (numerical) model. If successful, the model equations may reveal causal relations.
- Quantify parameters related to system evolution (growth rates, damping rates).
- Use techniques such as correlations, conditional averages; these linear analysis techniques by themselves cannot reveal causality, but additional reasoning (based on physical insight or models) may allow drawing conclusions.
In the fusion context, see [4].
Analysis techniques
Several techniques have been elaborated to quantify Wiener's causality on the basis of measured time series. [5]
Recently, a specific technique taken from Information Theory (the Transfer Entropy)[6] was applied succesfully to fluctuation data from fusion devices. [7]
References
- ↑ Causality
- ↑ Causality_(physics)
- ↑ N. Wiener. The theory of prediction. Modern Mathematics for Engineers, Mc-Graw Hill, New York, 1956, ISBN 0486497461
- ↑ K.H. Burrell, Tests of causality: Experimental evidence that sheared flow alters turbulence and transport in tokamaks, Phys. Plasmas, 6(12):4418, 1999
- ↑ K. Hlaváková-Schindler, M. Palus, M. Vejmelka, and J. Bhattacharya. Causality detection based on information-theoretic approaches in time series analysis, Phys. Reports, 441(1):1, 2007
- ↑ T. Schreiber, Measuring information transfer, Phys. Rev. Lett., 85(2):461, 2000
- ↑ B.Ph. van Milligen, G. Birkenmeier, M. Ramisch, T. Estrada, C. Hidalgo, and A. Alonso, Causality detection and turbulence in fusion plasmas, Nucl. Fusion 54 (2014), 023011
