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

[Alexandre Gramfort]

hi Per,

if you simulate with an MVAR then you have stationary sources so I
would first experiment with MxNE or Gamma-MAP.

However you are in unexplored territories ...

Alex


On Fri, Jul 11, 2014 at 1:07 AM, Per Arnold Lysne <lysne at unm.edu> wrote:
> 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.
>
> Cheers,
> Alex
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