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

[Alexandre Gramfort]

hi Per,

>     I've been working through the mechanics of TF-MxNE this weekend, and I think I can answer two recent questions I have asked:
>
>     With regard to TF-MxNE and Granger Causality, it seems to me that this should work. The mathematics of the localizations themselves may be non-linear, but Eqns. 3 and 4 from Gramfort et al. (2013) appear to be completely linear. Therefore, a linear system of sources within the brain are linearly projected onto the sensors by the forward solution, and then Eqn. 3 (solved for X) brings an estimate of them back into brain space and the structure of the system should not be disturbed?

the forward is always linear indeed. It's the inverse / source
estimation which is not.

>     With regard to individual trial output, the estimate Z* from Eqn. 4 could be determined based on an average evoked response, but then applied to individual trials in sensor space to determine timecourses for these trials at the already established locations?

what would make sense would be to use the spatiotemporal
atoms/coefficient estimated on the evoked and run a least square fit
for only these atoms on each trial.
It's however not implemented.

>     Does this make sense, or can you see a flaw with my reasoning?
>
>     Also, looking at Figure 6 panel d) in (2013), are these timecourses completely positive by coincidence, or is the magnitude taken?
> Around 50 and 150ms both approach zero and then abruptly turn upward as if the absolute value were being plotted?

it's amplitude as these results were obtained with loose orientation.

HTH

Alex