# 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

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 $ E \times B $ 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