Input Identification in the Ornstein-Uhlenbeck Neuronal Model with Signal Dependent Noise

The Ornstein-Uhlenbeck neuronal model is investigated under the assumption that the amplitude of the noise depends functionally on the signal. This assumption is deduced from the procedure in which the model is built and it corresponds to commonly accepted understanding that with increasing magnitude of a measured quantity, the measurement errors (noise) are also increasing. This approach based on the signal dependent noise permits a new view on searching an optimum signal with respect to its possible identification. Two measures are employed for this purpose. The first one is the traditional one and is based exclusively on the firing rate. This criterion gives as an optimum signal any sufficiently strong signal. The second measure, which takes into the account not only the firing rate but also its variability and which is based on Fisher information determines uniquely the optimum signal in the considered model. This is in contrast to the Ornstein-Uhlenbeck model with constant amplitude of the noise.