Dear Chin Wei,
As you point out the error components e_i at voxel i are distributed as
p(e_i) = N(e; 0, sigma_i^2 V)
where V = sum_j \lambda_j Q_j
1. The hyperparameters \lambda_j are estimated using the ReML/EM
algorithm described in equation A.5 of
http://www.fil.ion.ucl.ac.uk/~wpenny/publications/bayes1.pdf
They are set so as to maximise the 'ReML objective function'.
This is equivalent to the probability of the data given the model after having
integrated out the parameters (regression coefficients).
These parameters are computed once, for the whole volume of data.
- when you press ESTIMATE in SPM, this will be the first step -
hyperparameter estimation.
2. \sigma_i^2 is then a voxel-wise scaling of V that best fits
the data at voxel i
3. Details of the principles underlying how the T and F statistics are
derived are given in the paper
http://www.fil.ion.ucl.ac.uk/spm/doc/papers/sjk_heuristic.pdf
I am afraid this is a rather technical area.
Let me know how you get on.
Best,
Will.
chin wei wrote:
> Hi all. I have some questions reading Human Brain Function. The
> questions described in the attachment.
--
William D. Penny
Wellcome Department of Imaging Neuroscience
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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