[Mne_analysis] [Freesurfer] question about how to calculate COV for MNE
Hari Bharadwaj
hari at nmr.mgh.harvard.edu
Mon Apr 7 10:01:15 EDT 2014
Hi Joe,
Thought I'll mention a couple of things that might help understand the scaling etc.
(1) the noise cov that is computed and stored in the -cov.fif files corresponds to the covariance of the measurement noise in the *raw* data and hence when using it to localize multitrial *averaged* evoked responses, it is scaled by the number of trials in the average (based on the assumption that noise is independent from trial to trial and hence scales that way).. Look for the "nave" input when generating "stc" files.
(2) whether you add or subtract two *average* evoked responses, the resulting noise distribution is the same (i.e., still mean zero and variance depending on the numbers of trials in each condition).. More generally when you take an arbitrary linear combination of two or more averaged responses, the mean is still zero for the noise and the variance scales depending of the weights for each condition and numbers of trials that went into the corresponding averages.
(3) based on (2), considering the common special case of a difference response of two (separately averaged) conditions, if the number of trials in each of the two conditions that went in were not the same and are instead L1 and L2 respectively, then the effective scaling of the noise (from raw to the difference waveform) variance is what is calculated as Leff.
HTH,
Hari
Hari Bharadwaj
PhD Candidate, Biomedical Engineering,
Auditory Neuroscience Laboratory
Boston University, Boston, MA 02215
Martinos Center for Biomedical Imaging,
Massachusetts General Hospital
Charlestown, MA 02129
hari at nmr.mgh.harvard.edu
Ph: 734-883-5954
> On Apr 6, 2014, at 11:40 PM, Joseph Dien <jdien07 at mac.com> wrote:
>
> I should say Python, not C++…
>
>> On Apr 6, 2014, at 11:31 PM, Joseph Dien <jdien07 at mac.com> wrote:
>>
>> Fair enough! Just trying to understand what Section 6.3 is trying to communicate. So let me try another possible interpretation:
>>
>> Compute the COV for the two conditions. When subtracting the two conditions, the accompanying COV matrix (same for both conditions since they were pooled when computing it) is divided by Leff. Likewise the accompanying degrees of freedom (used if it is subsequently averaged together with another COV matrix per Section 4.17) is set equal to Leff.
>>
>> Not saying this is a procedure that makes sense to me either, just asking what the intent is of the MNE developers. Based on your response, this is currently my best guess, although it doesn’t make sense to me either since dividing the COV matrix by a single scalar (however computed) shouldn’t affect computations about relative noise levels in the channels. Basically, I’m not sure what is being done with COV so it’s hard for me to judge what is a reasonable interpretation of Section 6.3.
>>
>> I appreciate the link to the code, but since I’m a Matlab programmer not a C++ programmer, it’s very hard for me to parse the code. If someone could just tell me what is to be done according to 6.3 when computing a difference wave rather than just what not to do, this would be greatly appreciated. I’m trying to add support for FIFF file format to my Matlab EEG software analysis suite (http://sourceforge.net/projects/erppcatoolkit/) and want to make sure I’m doing it in a manner that would be acceptable to the MNE developers, for the benefit of the users of my package.
>>
>> Thanks for taking the time to read my question!
>>
>> Joe
>>
>>
>>
>>> On Apr 5, 2014, at 5:51 AM, Alexandre Gramfort <alexandre.gramfort at telecom-paristech.fr> wrote:
>>>
>>> hi joe,
>>>
>>>>> I have a question about how to calculate the COV for the MNE software.
>>>>> As I understand it from Section 4.17 of the 2.7.3 MNE manual, if one is
>>>>> averaging together COV matrices, one weights them by the number of
>>>>> observations going into each one. I also see from Section 4.17.2 that these
>>>>> are technically not covariance matrices so much as sum-of-squares matrices
>>>>> where the epochs going into each variable has been baseline corrected.
>>>>>
>>>>> Assuming my understanding so far is correct, my question is about how to
>>>>> proceed when making linear combinations of COV matrices, as in a difference
>>>>> wave, as discussed in Section 6.3. Would the following be the correct
>>>>> procedure?
>>>>>
>>>>> Compute the COV separately for the two conditions (say standard and rare
>>>>> oddballs). Subtract the two COV matrices to obtain C0.
>>>
>>> Subtracting two COV matrices is a bad idea. You can make the new cov
>>> non positive.
>>>
>>> basically the noise cov is just to estimate the noise so any sample you use
>>> to get a better estimate the better. There is no condition or contrast
>>> at this stage.
>>>
>>> for source reconstruction you should use the same noise cov for the two
>>> conditions to have the same inverse operator.
>>>
>>> you can look at this file to know more about the internals:
>>>
>>> https://github.com/mne-tools/mne-python/blob/master/mne/cov.py
>>>
>>> HTH
>>> Alex
>>>
>>>
>>>>> Then calculate C by
>>>>> dividing by Leff, which in turn is calculated as Leff= (L1*L2)/(L1+L2) where
>>>>> L1 is the number of observations in the first COV matrix and L2 is for the
>>>>> second.
>>>>>
>>>>> But if done in this way, the two COV matrices would not be weighted by
>>>>> their relative sample sizes. So would I also weight them by L1 and L2
>>>>> during the subtraction, as done for averaging per 4.17? But then what is
>>>>> the purpose of the Leff calculation? Or is the idea that one would calculate
>>>>> a single COV based on both conditions and then one would modify COV by Leff
>>>>> to reflect that the signal-to-noise ratio has been reduced by combining two
>>>>> averages with differing sample sizes? But in the case where both samples
>>>>> equal, say, 10, Leff would end up equalling 100/20=5. Dividing C by 5 seems
>>>>> like too much. Anyway, very confused. Any guidance would be appreciated.
>>>>>
>>>>> Respectfully,
>>>>>
>>>>> Joe
>>>>>
>>>>>
>>>>>
>>>>>
>>>>> --------------------------------------------------------------------------------
>>>>>
>>>>> Joseph Dien,
>>>>> Senior Research Scientist
>>>>> Maryland Neuroimaging Center
>>>>> University of Maryland
>>>>>
>>>>> E-mail: jdien07 at mac.com
>>>>> Phone: 202-297-8117
>>>>> http://joedien.com
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
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>>
>> --------------------------------------------------------------------------------
>>
>> Joseph Dien,
>> Senior Research Scientist
>> Maryland Neuroimaging Center
>> University of Maryland
>>
>> E-mail: jdien07 at mac.com
>> Phone: 202-297-8117
>> http://joedien.com
>
>
> --------------------------------------------------------------------------------
>
> Joseph Dien,
> Senior Research Scientist
> Maryland Neuroimaging Center
> University of Maryland
>
> E-mail: jdien07 at mac.com
> Phone: 202-297-8117
> http://joedien.com
>
>
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