Fig. 4.

Conditional estimates using a stochastic model: This figure shows similar results to those presented in Fig. 3. However, in this case the conditional estimates were based upon a stochastic model using Generalised Filtering. Here (upper left), we see that the estimates are closer to their true values and are much more precise. Furthermore, the conditional (maximum a posteriori; MAP) estimates of the neuronal fluctuations are very close to those elicited by the neuronal input used to simulate the data (compare the left and right lower panels). Because this model includes unknown (hidden) neuronal and physiological states, it also returns a conditional estimate of the hidden states causing responses. These are shown in the upper right panel. The conditional expectations are shown as coloured solid lines and the 90% confidence intervals (tubes) are shown as grey regions. Note that these hidden states are effectively log-states, such that a value of zero corresponds to 100% of the steady-state value. For small deviations from zero, the values of these hidden states correspond roughly to proportional changes. In this example, we see changes of up to about 20% (in blood flow).