# Causality detection

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 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 $E \times B$ 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