Stewart Denslow wrote:
> Dear DCM architects,
>
> In choosing a bilinear approximation in DCM, do you have a rationale for
> including the cross term but not the squared terms? I am aware that it is a
> widely used approximation (outside of the SPM world) but I am also aware
> that there is often some reason to believe that the squared terms are
> negligeable.
> Is there such an argument for functional imaging?
At present the bilinear approximation in DCM is
dz/dt= (a+bu)z + cu
Including the squared terms would make it
dz/dt = (a+bu) z + c u + e z^2 + f u^2
The nonlinear term in the input could be accomodated by
postulating extra inputs.
However, the nonlinear state term (e z^2) results in
a truly nonlinear dynamical model.
Such a model has rich dynamics and is surely much
closer to neuronal time series than the model
currently implemented in DCM. But, the parameters
of such a model could not be identified from fMRI
data.
We are currently, however, investigating such DCMs
for the analysis of EEG.
Best wishes,
Will.
>
> Thanks,
> Stew Denslow
>
>
>
--
William D. Penny
Wellcome Department of Imaging Neuroscience
University College London
12 Queen Square
London WC1N 3BG
Tel: 020 7833 7475
FAX: 020 7813 1420
Email: [log in to unmask]
URL: http://www.fil.ion.ucl.ac.uk/~wpenny/
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