Dear Yury,
>> ---------------------------------- Dear All,
>>
>> I have a conceptual concern regarding the MSP algorithm used by
>> SPM8 to localize sources of EEG/MEG activity. The algorithm is
>> based, in part, on EM iterative scheme used to estimate source
>> priors (source covariance matrix) from the measurements. The way
>> this scheme is described in the Phillips et al. 2002 paper, it
>> works as an iterative Bayesian estimator: first it estimates the
>> sources, then calculates the resulting source covariance from the
>> estimate, next it (effectively) uses it as the new prior for the
>> sources, estimates the sources again, etc. However, applying
>> Bayesian learning iteratively is a common pitfall and should not be
>> used, because each such iteration amounts to introducing new
>> fictitious data. I attached a nice introductory paper illustrating
>> the pitfall on page 1426.
I don't believe that this is a pitfall.
The parameters of the prior (specifically the variance components) are
estimated iteratively along with the variance components of the likelihood.
Importantly, each is estimated using degrees of freedom which are
effectively partitioned into those used to estimate prior variance and
those used to estimate noise variance. This is a standard Empirical
Bayesian approach and produces unbiased results.
See papers by David Mackay on this topic and eg. page 6-8 of the chapter
on 'Hierarchical Models' in the SPM book (this is available under
publications/book chapters on my web page
http://www.fil.ion.ucl.ac.uk/~wpenny/ - note gamma and (k-gamma) terms
in denominator of eqs 32 and 35 denoting the partitioning of the degrees
of freedom).
Nevertheless, I'd like to read page 1426 of your introductory paper. Can
you send it to me ?
Best wishes,
Will.
In particular, the outcome of the
>> iterations may become biased toward the original source covariance
>> used. In my test application of the described EM algorithm I found
>> that scaling the original source covariance matrix changes the
>> resulting sources estimate, which, in principle, should not happen.
>> For comparison, this problem does not occur, when the source
>> covariance parameters are learned using ordinary or general
>> cross-validation (OCV or GCV).
>>
>> Best, Yury
>>
>>
>>
>>
>>
>>
>
>
--
William D. Penny
Wellcome Trust Centre for Neuroimaging
University College London
12 Queen Square
London WC1N 3BG
Tel: 020 7833 7475
FAX: 020 7813 1420
Email: [log in to unmask]
URL: http://www.fil.ion.ucl.ac.uk/~wpenny/
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