Dear Jagath
> you wrote
>
> > Even if raw fMRI data were
> > not well behaved, they can be made so by trivial pre-processing (e.g.
> > subsampling and spatial convolution).
> >
> The idea here is to Gaussianize SPMs so that GRF theory is valid.
Yes. In fact the idea is to 'Gaussianize' the data (signal plus error)
through central limit theorum so that GRF can be applied.
[We used to 'Gaussianize' SPMs using the probability integral transform
to make a SPM{t} into a SPM{Z} but this is another issue.]
Central limit theorum suggests that when you add several variables
together the sum is normally distributed even if the original variables
were not. If you add about 12 variables the distribution is generally
indistinguishable from a Gaussian distribution. This rule of thumb is
a bit like not being able to fold a piece of paper more than 7 times.
Therefore, if your smoothing kernel encompasses about 12 voxels, the
result will approximate a Gaussian field. This corresponds to a FWHM
of about 12^(1/3) = 2.28 voxels.
> Are we intentionally changing raw data here? Could any random field
> be made GRF in this way?
Yes - absolutely.
I hope this helps - Karl
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