[Mne_analysis] Are TF-MxNE timecourses appropriate for Granger causality?

[Alexandre Gramfort]

hi Per,

>     I am looking for a sparse MEG inverse solution that would be appropriate
> for input to Granger causality analysis. In particular, since Granger
> causality is usually implemented by linear means, would the output from a
> non-linear, sparse inverse solution such as TF-MxNE be appropriate here?

TF-MxNE achieves an adaptive non-stationary filtering of evoked data
built in the source localization algorithm.

Granger causality with AR models are not playing nice with filtered
data and work on single trial or raw data AFAIK.

It is therefore unclear what can happen if you apply GC after TF-MxNE.

> I have not been able to determine this from Gramfort's 2013 NeuroImage paper
> or other sources (probably  because of my own mathematical shortcomings). In
> particular, I cannot tell if the non-linearity in TF-MxNE is limited to the
> localizations (which would be acceptable) or if it applies to the
> corresponding timecourses as well (in which case I would expect it to
> disrupt linear Granger analysis).

the non-linearity is also temporal as an entire time interval of data
is processed together.

>     I am using the non-parametric Granger causality methods of Dhamala,
> Rangarajan, and Ding (Physical Review Letters, NeuroImage, 2008, where
> Wilson's 1972 numerical spectral decomposition is used in place of MVAR
> estimation), and the ability of TF-MxNE to work with non-stationary data is
> very appealing.

hum... Maybe I should look into it.

let me know if you make any progress.

Cheers,
Alex