[Mne_analysis] equivalence of averaged single trial STCs and evoked STCs

[Hari Bharadwaj]

Hi Alex,
   Thanks for the gist! Just ran it.. The results actually see to suggest
that the two stc (one with the original nave of 55, and the new nave of
10000) are pretty much scaled versions of each other with the scale
factor being exactly what you would expect, namely the ratio of the
sqrt(nave) in the two cases:
 See: http://nmr.mgh.harvard.edu/~hari/MNEnotes/dSPM_nave_scaling.pdf

I agree with you that the regularization would change the numerical values
very slightly and hence they won't be *exactly* equal.


Also, I do think dSPM is pretty much z-scoring when you use the baseline
periods to estimate the noise covariance. If w_i is the row of the inverse
operator corresponding to the weights needed to estimate the MNE of source
#i, and C is the noise covariance, then the normalization factor used in
dSPM for that source is:
sqrt(w_i*C*w_i.T) (where .T denotes a transpose), which is indeed the
estimated standard deviation of the baseline. The reason that the dSPM
standard deviation is not *exactly* equal to 1 in the baseline is that the
noise-cov is estimated from raw-data samples and scaled by 'nave' =
#trials_in_evoked, rather than being estimated from the baseline of the
evoked data.
  On the other hand, if you had many datasets/sources and calculated the
baseline standard deviation, then across the datasets/sources you would
have the baseline sample standard deviation be distributed narrowly
around 1. In other words, the dSPM has a "null distribution" that is
mean zero and variance 1, which is what makes it an "SPM".

What am I missing?

Thanks,
Hari




On Sun, March 16, 2014 4:08 am, Alexandre Gramfort wrote:
> hi Hari,
>
>>     Just to follow up on your comment.. What do you mean when you say,
>> that dSPM is "not a plain scaling of the estimates"?
>
> yes it is. I wasn't clear. What I meant is that when you change nave you
> don't just change the scale of dSPM. At least numerically it is not the
> case
> as confirmed by a tiny experiment.
>
> https://gist.github.com/agramfort/9579975
>
>> For any *given vertex*, the MNE time course and the dSPM time course (or
>> any other linear inverse time course) are indeed different only by a
>> scale factor.  Of course, the MNE and dSPM *spatial maps* are not scaled
>> versions of each other because the multiplier that relates the dSPM
>> estimates to the MNE estimates is different for each vertex (the point
>> of noise normalization being to improve the spatial map).
>
> yes no confusion here.
>
>> Also, if the baseline period is used for noise cov estimation, it is not
>> clear to my why post hoc normalization by the baseline standard
>> deviation is different from dSPM (even mathematically)..
>
> dSPM is not exactly a z-scoring.
> if it were the case the std deviation of each time course during
> baseline would be exactly 1.
> Also when you use a noise cov in dSPM, you often add a regularization
> and the inverse code clips the tiny eigenvalues.
>
> Alex
>
>
>


-- 
Hari Bharadwaj
PhD Candidate, Biomedical Engineering,
Boston University
677 Beacon St.,
Boston, MA 02215

Martinos Center for Biomedical Imaging,
Massachusetts General Hospital
149 Thirteenth Street,
Charlestown, MA 02129

hari at nmr.mgh.harvard.edu
Ph: 734-883-5954