Steve,
>
> Dear SPMers:
>
> >From the literature, I gather that temporal smoothing is usually performed
> by convolving a voxel's time series with a Gaussian whose scale is the same
> as that of the hemodynamic response.
>
> One thing troubles me; this convolution doesn't "preserve causality." That
> is, the value at time t will influence the smoothed values at times s>t.
>
> (1) Does this matter? I'm not comfortable with it, in that if you're doing
> an event-related analysis, information about a hemodynamic response's onset
> is "leaked" into the past.'
No, it does not matter because inference is now on the filtered time series.
The filter (including all lag info) is implicitly represented in the
linear model used for inference. A corollary is that one could apply
arbitrary lags. In fact, one could even apply a kernel after varying the
phases differently at different frequencies with no effect at all on
inference. That is, it is only the magnitiude spectrum of the kernel that
is important on filtering's effects on making statistical inference more
robust.
> (2) Why not just use a filter which is causal? I.e., if we're filtering by
> convolution, say signal f(t) is replaced by f*g(t), where g is usually a
> gaussian, why not use a g satisfying g(s) = 0 for s>0? (I don't have a EE
> background, so maybe those in the trade will have valid objections.)
Ignoring the technicality that g(s) might not equal 0 for any s, yes
you could theoretically lag g(s) such that it is (almost) causal. But again
this would yield equivalent inference to the case in
which filtering used any other lag (including 0 lag).
Sincerely,
Eric
Eric Zarahn
University of Pennsylvania
> --Steve Fromm, NIDCD
>
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