Speaker:
Angelo Vulpiani
Title:
Understanding causation via correlations and linear response theory
Abstract:
In spite of the (correct) common- wisdom statement correlation does not imply causation, a proper employ of time correlations and of fluctuation- response theory allows to understand the causal relations between the variables of a multi-dimensional linear Markov process.
The fluctuation- response formalism can be used both to find the direct causal links between the variables of a system and to introduce a degree of causation, cumulative in time, whose physical interpretation is straightforward.
In absence of the knowledge of vector which describes the state of the system,
only from the time series a quite natural approach is the use of the embedding methodology, unfortunately in general for stochastic processes such a procedure cannot be exact.
Although for generic non- linear dynamics there is no simple exact relationship between correlations and response functions, the described protocol can still give a useful proxy also in presence of weak nonlinear terms.