Hi Ged,
let's wait and see if there is a "fundamentalist Topologist" around ;-)
In the meantime, those interested by the discussion can have a look at
the following papers to get the background picture:
* Topological inference for EEG and MEG data, Kilner et al, Annals of
Applied Statistics, in press:
http://www.e-publications.org/ims/submission/index.php/AOAS/user/submissionFile/5651?confirm=973db4b7
* Topological FDR for neuroimaging, Chumbley et al, NeuroImage, 2010:
http://dx.doi.org/10.1016/j.neuroimage.2009.10.090
* False discovery rate revisited: FDR and topological inference using
Gaussian random fields, Chumbley et al, NeuroImage, 2009:
http://dx.doi.org/10.1016/j.neuroimage.2008.05.021
Best regards,
Guillaume.
DRC SPM 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.
>
> 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, Joćo 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,
>>>>
>>>> Joćo
>>>>
>>>> On Thu, May 6, 2010 at 11:42 AM, DRC SPM <[log in to unmask]> wrote:
>>>>> Dear Joćo,
>>>>>
>>>>> 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 Joćo 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,
>>>>>>
>>>>>> Joćo
>>>>>>
--
Guillaume Flandin, PhD
Wellcome Trust Centre for Neuroimaging
University College London
12 Queen Square
London WC1N 3BG
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