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

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

Best wishes,
Ged

On 6 May 2010 12:50, Guillaume Flandin <[log in to unmask]> wrote:
> Hi Ged,
>
>> Depends on what particular set of p-values you are interested in...
>> (which I think is why SPM shows the (unique) t-values instead, as you
>> say).
>
> or because p-values are attributed to topological features of the field
> and not to each and every voxel.
> I'm not sure to see what an image of p-values could be but am happy to
> be enlightened ;-)
>
> All the best,
> Guillaume.
>
>
>> It's easy to convert a t-map to a map of uncorrected voxel-wise
>> p-values (I think both Volkmar's Volumes toolbox and Christian's VBM
>> toolboxes have this functionality, or you can do it with imcalc).
>>
>> It's also easy to convert the above uncorrected p-map to a voxel-wise
>> FDR p-map (or q-map), though it was a bit slow with spm_P_FDR last
>> time I tried (you've just reminded that I have a much faster version
>> of this, that I should probably inlclude in a future update...).
>>
>> RFT voxel-wise FWE p-values are fairly easy to get from spm_P, though
>> if I remember correctly, you can get NaNs (perhaps even errors) with
>> very small t-values, which might need sorting out before you saved the
>> image for later visualisation. This might have been fixed since the
>> last time I tried though.
>>
>> Cluster-wise p-values are not so easy to get, and would require a bit
>> of coding. Also, they would not show you any information about
>> relative signal within the clusters, whereas SPM's use of voxel-wise
>> t-values within significant clusters gives you a little extra
>> information.
>>
>> Finally, note that overlaying p-values in e.g. MRIcroN will probably
>> not look good, firstly because more significant values are smaller,
>> whereas most colour-maps expect larger=better, and secondly because
>> the difference between 0.1 and 0.01 will probably end up being a very
>> small difference in the colour-map, while it's actually a very
>> important difference. One way to deal with this is to use
>> abs(log10(p)) instead of p, then e.g. 0.1 maps to 1, 0.01 maps to 2,
>> and the overlays look reasonably nice. The only complication with this
>> is that 0.05 maps to 1.301, so if this is the alpha-level you are
>> interested in, labelling the colour-bar with this value might look a
>> bit messy.
>>
>> All things considered, it's probably not worth all this trouble, as
>> the thing you are usually interested in is which blobs survive a
>> particular significance threshold. There's also an argument that the
>> best thing you could look at within these blobs is the raw contrast
>> image, rather than the t-values or (any of) the p-values:
>> http://www.fil.ion.ucl.ac.uk/spm/ext/#MASCOI
>>
>> Best,
>> Ged
>>
>>
>> On 6 May 2010 12:11, João Duarte <[log in to unmask]> wrote:
>>> Dear Ged,
>>>
>>> thank you very much. It was easy...
>>> By the way, as far as I understand, the colorbar displayed is the one with
>>> the T values, right? Is it possibe to show a colorbar with p-values instead?
>>>
>>> Thanks.
>>>
>>> Regards,
>>>
>>> João
>>>
>>> On Thu, May 6, 2010 at 11:42 AM, DRC SPM <[log in to unmask]> wrote:
>>>> Dear João,
>>>>
>>>> When you've got the glass brain results up in SPM, click the "save"
>>>> button near the bottom right of the interactive window, and enter a
>>>> filename for the output image. You should then be able to load this
>>>> thresholded t-map as an overlay in MRIcroN etc.
>>>>
>>>> Note that you can display the blobs overlaid on an image in SPM itself
>>>> too, just click the "overlays..." menu, and pick "sections" and then
>>>> select an image you want to overlay onto (e.g. an average image,
>>>> created by warping your original images with the same transformations
>>>> used to create your VBM data, and then using imcalc with expression
>>>> mean(X) and the data matrix (dmtx) flag true). If you've used DARTEL,
>>>> the simplest thing to overlay onto is the GM of the final template,
>>>> e.g. Template_6.nii.
>>>>
>>>> Hope that helps,
>>>> Ged
>>>>
>>>> 2010/5/6 João Duarte <[log in to unmask]>:
>>>>> Dear SPMers,
>>>>>
>>>>> how can I display the map of significant blobs that is output of VBM
>>>>> analysis in SPM8, using for example MRIcroN?
>>>>>
>>>>> Thanks in advance.
>>>>>
>>>>> Regards,
>>>>>
>>>>> João
>>>>>
>>>
>>
>>
>
>
> --
> Guillaume Flandin, PhD
> Wellcome Trust Centre for Neuroimaging
> University College London
> 12 Queen Square
> London WC1N 3BG
>