Hi all,

I received several off-list replies to my questions, and have been
meaning to post a summary for some time.

> I understand from "Voxel-Based Morphometry -- The Methods" that cluster
> size inference is invalid for VBM due to the nonstationarity of the
> residual smoothness.
> (See p9 of the PDF at http://dx.doi.org/10.1006/nimg.2000.0582 )

None of my off-list replies questioned this.

> Doesn't FWE / Random Field correction also assume stationary smoothness
> (i.e. constant resels/voxel over the image)?

Some respondents argued that SPM does use a non-stationary roughness
estimate in the form of the Resels Per Voxel. The theory of this has
been expounded in e.g.

  http://www.math.mcgill.ca/~keith/smoothness/techrept.pdf
  http://dx.doi.org/10.1006/nimg.1999.0508

However, there doesn't seem to have been an official follow-up
regarding SPM's use of the RPV image/values discussed in this thread:

  http://www.jiscmail.ac.uk/cgi-bin/webadmin?A2=ind0612&L=SPM&P=8750

It seems that currently, in both SPM2 and SPM5, the RPV estimate is
*never* used, due to a typo in the code.

It also remained slightly unclear to me from the extremely helpful
messages of Satoru Hayasaka:

  http://www.jiscmail.ac.uk/cgi-bin/webadmin?A2=ind0612&L=SPM&P=13193

whether fixing this typo will result in changes to the table of
voxel-level FWE-corrected p-values or just to the cluster-level
FWE-corrected ones. But it's quite possible that I am asking a stupid
question here...

> And if so -- even if it
> remains approximately valid -- doesn't this weigh heavily in favour of
> FDR, which avoids the question of smoothness?

I received mixed responses to this suggestion. Most replies did seem
to prefer FDR due to its reduced assumptions. One correspondent (I'll
assume they want to remain anonymous since they could have posted to
the list themselves, in the first place) suggested that the fact that
FDR ignores smoothness may be a problem. However, someone else pointed
out that FDR is valid, not only for independent voxels, but also for a
fairly general case of correlated noise, which most likely includes
typical smoothed imaging data -- see:
  http://dx.doi.org/10.1006/nimg.2001.1037
and some helpful commentary in:
  http://www.wbic.cam.ac.uk/~amw71/publications/TMI2004.pdf

> FDR seems to be preferred by some in the FMRI community mainly because
> it is generally a less stringent correction;

There was an objection to this comment, with the view instead being...

> I'd be interested to hear
> whether people agree that for VBM FDR might also be preferable on more
> fundamental grounds, due to its lack of smoothness assumptions?

...that this is probably true.

Additionally, some people expressed dissatisfaction not simply with
Random-Field based FWE-correction but also with parametric testing
itself. Instead, several respondents seemed to favour non-parametric
testing as implemented in e.g. SnPM, CamBA, and randomise:

  http://www.sph.umich.edu/ni-stat/SnPM/
  http://sourceforge.net/projects/camba
  http://www.fmrib.ox.ac.uk/fsl/randomise/index.html

On the other hand, someone suggested that spatially-adaptive RF/FWE
correction using RPV would not differ much from the standard
stationary RF correction, and appeared to imply that the latter was
probably good enough.

> I'd also be interested to hear from anyone who thinks I am talking utter
> nonsense ;-)

Surprisingly, no-one seemed to suggest this, at least not in any
emails they sent to me...

Many thanks to everyone who replied. I hope that this summary will be
of interest to some people. I am in no way claiming to present a
definitive conclusion on this topic, and would welcome further
comments and debate.

Best wishes for the holidays,
Ged.