Dear Roy
I think that the main argument would be that the intrinsic volume has not changed.
The intrinsic volume is the resel count and in 1D is just the number of data points (say N) in a curve divided by the smoothness (FWHM in data points). i.e. N/FWHM
So if you interpolate in twice as many data points (say) then N doubles but so does FWHM hence the intrinsic volume and all the thresholds stay the same.
Here are some papers which may say this more elegantly :
J.M. Kilner, K.J. Friston. Topographical inference for EEG and MEG. Ann. Appl. Stat., 4 (3) (2010), pp. 1272–1290
And this one talks a bit more about intrinsic volume:
Best
gareth
Dear all,
We are addressing some reviewer comments regarding the use of random field theory for EEG. One of the the assertions made by our reviewer is that, because of the interpolation step needed to map electrode locations (128 in our case) onto a 2D grid/image
(65*65 in our case) to be used in SPM, we're essentially increasing the number of statistical tests we need to correct for.
We want to argue that the number of tests we need to correct for is estimated based on the smoothness of the statistical map. One sub-argument here would be that interpolating data points in between electrode locations does not result in reduced smoothness
(relative to the original EEG-based data). At least, that's how it seems to us intuitively. Is there any expert out there who has a more formal take on this?
Best,
Roy
--
Roy Cox, M.Sc. | Brain & Cognition Group | Department of Psychology | University of Amsterdam
| Weesperplein 4 | 1018 XA Amsterdam
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