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.


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Traditional approaches to the determination of causal relationships between various (fluctuating) variables include a wide range of methods.
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.
* 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 charactaristic events.
* 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.
* 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).
* 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 additioal reasoning (based on physical insight or models) may allow drawing conclusions.   
* 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>.
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 ==
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<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 '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.  
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

  1. ↑ Causality
  2. ↑ Causality_(physics)
  3. ↑ N. Wiener. The theory of prediction. Modern Mathematics for Engineers, Mc-Graw Hill, New York, 1956, ISBN 0486497461
  4. ↑ K.H. Burrell, Tests of causality: Experimental evidence that sheared flow alters turbulence and transport in tokamaks, Phys. Plasmas, 6(12):4418, 1999
  5. ↑ 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
  6. ↑ T. Schreiber, Measuring information transfer, Phys. Rev. Lett., 85(2):461, 2000
  7. ↑ 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
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