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\end{align}</math>
The first line describes the change in neural activity <math>z</math> with respect to time (i.e., <math>\dot{z}</math>), which cannot be directly observed using non-invasive functional imaging. The evolution of neural activity over time is controlled by neural function <math>f</math> with parameters <math>\theta^{(n)}</math> and experimental inputs <math>u</math>. The neural activity in turn causes the timeseries <math>y</math>, written on the second line. This is controlled by observation function <math>g</math> with parameters <math>\theta^{(h)}</math>. Additive observation noise <math>\epsilon</math> completes the model. Of key interest to experimenters are the neural parameters <math>\theta^{(n)}</math> which, for example, represent the change in connection strengths due to experimental conditions.
Specifying a DCM requires selecting models <math>f</math> and <math>g</math> and setting appropriate [[Prior probability|priors]] on the parameters - e.g. selecting which connections should be switched on or off. The choice of which models to use depends on the hypotheses being tested and the type of data which is available. For example, with fMRI, <math>f</math> is a simple differential equation model of effective connectivity and <math>g</math> is a detailed biophysical model of the [[Haemodynamic response|BOLD response]]. The rest of this section surveys the models which have been developed using the DCM framework.
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