Alexandre thank you for your reply. It did help. I now understand why
dSPM and sLORETA results differ even though MNE results do not. I am still
confused as to why MNE results do not change.
If I were to, say, go from millivolts to microvolts, then both the noise
and the data would be scaled by 1e3 and noise covariance matrix - by 1e6
and the SNR would stay the same. Same results of MNE with the same input
but scaled covariance mean that here - where the data is scaled by 1e3 as
well - I would get the source estimates scaled by 1e3 which is strange. I
would expect (from the formulas on The minimum-norm current estimates
<https://martinos.org/mne/stable/manual/source_localization/inverse.html>\)
that scaling of all the data should not change anything because the kernel
would have changed reciprocally - by 1e-3. What am I missing?
In my application I know the subject's structural information and electrode
locations beforehand but I do not know how the data that I get in real time
was preprocessed. At first, I used an identity covariance matrix to make
the inverse solution. Then I scaled it by the mean variance of all EEG
signals to tell mne-python the scale of the data but nothing changed, which
is what led me to this question. Just explaining that I do not multiply
random parts of the pipeline by random numbers 
Evgenii
From: Alexandre Gramfort <alexandre.gramfort at inria.fr>
To: Discussion and support forum for the users of MNE Software <
mne_analysis at nmr.mgh.harvard.edu>
Cc:
Bcc:
Date: Wed, 14 Feb 2018 21:15:10 +0100
Subject: Re: [Mne_analysis] MNE method is invariant to the scale of noise
if you change noise scaling you should change the SNR as it means you have
a lot worse SNR. the regularization parameter lambda is a function of the
snr
as you can see in the script.dSPM and sLORETA are like t-stat or f-stat. So if you multiply the cov by
1e6
then you will have dSPM and sLORETA solutions which are just divided by 1e3
(the scale of the standard deviation).HTH
AlexHi all,
I noticed that if I scale the noise covariance matrix, it does not change
the source estimates in any way. In this example
<https://martinos.org/mne/stable/auto_tutorials/plot_mne_dspm_source_localization.html#sphx-glr-auto-tutorials-plot-mne-dspm-source-localization-py> from
the example gallery if I change the method to "MNE" before the first stc
calculation and then do this:inverse_operator = make_inverse_operator(info, fwd, noise_cov,
loose=0.2, depth=0.8)
stc = apply_inverse(evoked, inverse_operator, lambda2,
method=method, pick_ori=None)from copy import deepcopy
noise_cov_scaled = deepcopy(noise_cov)
noise_cov_scaled['data'] *= 1000000
inverse_operator_scaled = make_inverse_operator(info, fwd, noise_cov_scaled,
loose=0.2, depth=0.8)
stc_scaled = apply_inverse(evoked, inverse_operator_scaled, lambda2,
method=method, pick_ori=None)Then stc_scaled contains exactly the same data as stc. With "dSMP" and
"sLORETA" the result do differ. Why doesn't "MNE" care about the scale of
the covariance matrix?Evgenii
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