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

Per Arnold Lysne lysne at unm.edu
Thu Jul 10 19:07:20 EDT 2014
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Hi Alex,

    I have tried to answer this question with a simulation, but am not completely sure I have done this right. I began with the "plot_simulate_evoked_data.py" example (http://martinos.org/mne/stable/auto_examples/plot_simulate_evoked_data.html#example-plot-simulate-evoked-data-py) and replaced the two wavelet-derived timecourses with a bivariate MVAR system which I generated using the "nitime" package. I commented out the IIR filtering but continued to use "generate_evoked" to create an evoked response which I then input to tf_mixed_norm (does this make sense? it feels like inputting something that is already in source space into the localizer algorithm). After ~250 iterations tf_mixed_norm reduces this system to two sources as expected, but both sources fall in the right hemisphere and an MVAR estimation of their timecourses no longer matches the system that I put it.

    In general I would like to simulate a simple MVAR system and assign it to a number of locations in brain space. Since TF-MxNE expects a sensor space evoked input, I think I would need to project this onto the sensor array? I would then like to pass this through TF-MxNE and see if the structure and locations of the original MVAR system are preserved. Does this sound like an appropriate way to approach this problem or am I missing something important?

    Thanks again,

Per Lysne
The University of New Mexico

PS: The non-parametric Granger causality method I mentioned below is implemented in Fieldtrip, although it may be an undocumented option.
From: mne_analysis-bounces at nmr.mgh.harvard.edu <mne_analysis-bounces at nmr.mgh.harvard.edu> on behalf of Alexandre Gramfort <alexandre.gramfort at telecom-paristech.fr>
Sent: Friday, July 4, 2014 1:46 PM
To: Discussion and support forum for the users of MNE Software
Subject: Re: [Mne_analysis] Are TF-MxNE timecourses appropriate for Granger     causality?

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.

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