Print

---

Hi Ged,

On 6 May 2010 14:21, DRC SPM <[log in to unmask] > wrote:

Hi Guillaume,

This is an interesting philosophical point... Personally, I am

slightly more "Voxelist" than I think Justin, Karl, and perhaps you

are... You might be surprised to hear that Keith was also Voxelist in

one pratical regard too, as SurfStat can indeed produce maps of RFT

corrected p-values for "peaks" and clusters, where these maps are

defined over all vertices or voxels. In the cluster case,

vertices/voxels have the uniform p-value of the cluster they are

contained in (or p=1, if they are outside a significant cluster), but

in the peak case, despite the arguments from the "Topologist" school,

Keith did assign FWE-corrected p-values to every vertex/voxel, and not

just the local maxima.

In fact, based on the lack of information within the clusters, Keith

came up with a nice visualisation which combines cluster and

vertex-wise significance, see e.g.

  http://www.stat.uchicago.edu/~worsley/surfstat/figs/Pm-f.jpg

I don't think he got around to implementing a similar visualisation

for voxel-wise data (SurfStatP returns the peak and cluster results

necessary, but I think you are on your own as to how to visualise

these), but I've seen no evidence that he had a philosophical

objection to this (especially not one that was somehow specific to the

voxel-wise but not vertex-wise case).

Similarly, in permutation testing, comparison to the null distribution

of the maximum over the image yields FWE-corrected p-values for every

voxel; you can choose to look at these only at local maxima voxels if

you wish, but no topological assumptions are required to control FWE.

In fact, being able to interpret individual voxels as significant is a

key distinction between weak and strong control of FWE made by e.g.

Nichols and Hayasaka (2003), p.422

  http://dx.doi.org/10.1191/0962280203sm341ra

Of course, this is all assuming that you can declare voxels as true or

false positives, which Justin and Karl have argued against... However,

I don't think their arguments have entirely convinced me that you can

declare local maxima or clusters as true or false either, if you can't

do so for voxels, since the same arguments about continuous and

infinitely extended signal would seem to screw up *all* notions of

type I and type II error, not just the voxel-wise ones.

Smoothing images with broad support (e.g. Gaussian) Kernels rides roughshod over the aspiration for strong control. Beyond this nit-picking, some of this depends on definition. Traditional RFT defines and controls false-positives under the null SPM. Under the null SPM all positives - no matter where they occur spatially - are false-positives. We considered a definition of false-positives that is more general, applying also under the alternative SPM (i.e. in the presence of experimentally-induced activations, even when these extend across the whole image). We followed the intuition that a false positive must generally be spatially removed from any underlying activation. To formalise this, take the example of peak inference. First interpret significant SPM peaks as indicating the existence of true signal peaks.  Let x indicate the distance between a discovered peak and the nearest true peak. Then any discovered peak beyond (predefined) distance x>c from a true peak is defined as false-positive (otherwise it is true-positive). Under the null SPM, we define x=inf for all discovered peaks (there are no underlying peaks). All discovered peaks are therefore spatial false-positives, in accordance with non-spatial definition of error. Importantly, false-positives are now also defined under the alternative SPM:  i.e. observed peaks farther than c from a true peak. Familywise false-positive error-rate and false-discovery rates can now be defined under the alternative SPM.

Note that this definition of a procedure’s spatial error-rate is derived from true/false classification of peaks. This classification is based on the spatial accuracy with which the procedure identifies target peaks in the underlying signal. Spatial accuracy can be therefore be examined and discussed per se. We took this perspective in the work Guillaume cited.

Finally, while the analysis of spatial error (or accuracy), applies most naturally to peak-level inferences using RFT, one may appraise the spatial accuracy of other procedures. Keith seemed happy with this (he was a co-author!), but I think it is rather questionable to preempt how he would have contributed to this debate now....


With my very best wishes

JC 
  

Perhaps a fundamentalist Topologist will reply to put me in my place?! ;-)

Best wishes,

Ged