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. 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'. 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 additioal reasoning (based on physical insight or models) may allow drawing conclusions.

In the fusion context, see .

Analysis techniques

Several techniques have been elaborated to quantify Wiener's causality on the basis of measured time series.

Recently, a specific technique taken from Information Theory (the Transfer Entropy) was applied succesfully to fluctuation data from fusion devices.