Dear Dr. Perry and John,
> >
> > Your particular criticism only applies if one is dealing with unknown
> > patterns of neuronal firing over at least several seconds. Even these will
> > often be adequately modelled by a box-car convolved with the haemodynamic
> > response function, since subtleties of the form of the neuronal response
> > may well be ironed out by the convolution. I can't imagine many
> > experimental designs in which one wishes to acquire whole-brain images in
> > which the selective averaging approach will still be advantageous,
>
> It is rare, but it does happen. We have encountered regions with
> unexpectedly long patterns of neuronal firing. And, as you say, these
> hemodynamic responses are well modeled by the impulse function convolved
> with a boxcar function. However, the experimenter must know the width
> of the boxcar a priori. This requirement biases the results since the
> only regions will be detected are those that satisfy this assumed width.
>
> This consideration is not important for the vast majority of studies.
> However, improved sampling obtained with basis functions is also
> only a slight benefit. You have a choice when you do a study: do you
> want a slight increase in sensitivity by using temporal basis functions
> (I am assuming that the TR is sufficiently short, say < 2.5 seconds), or
> do you want to be able to detect regions with unusual hemodynamic
> responses (and get an estimate of the hemodynamic response at each
> voxel). We have implemented both methods, so each investigator can
> choose the method he prefers. There is very little published data to
> guide this choice, so opinions tend to be very strongly held.
>
If selective averaging is equivalent to a linear model with a
kronecker delta basis set (I humbly note that I look forward to seeing
the proof of this), then the argument is not between averaging
and the GLM, but rather the choice of basis set. But the term
"basis" is being perhaps used loosely by our community
as it originally meant a set of (linearly independent) vectors
which span a vector space. Therefore, if we were using the term in
this fashion, then every basis set would be have equivalent
explanatory power, whether they comprise kronecker delta functions
or not. I guess the point that John is making is that the
space many of us assume for fMRI responses is incorrect such that
our "basis" sets are not really basis sets at all.
Eric
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