  We present a theoretical study aiming at model fitting for sensory neurons.
Conventional neural network training approaches are not applicable to this
problem due to lack of continuous data. Although the stimulus can be considered
as a smooth time dependent variable, the associated response will be a set of
neural spike timings (roughly the instants of successive action potential
peaks) which have no amplitude information. A recurrent neural network model
can be fitted to such a stimulus-response data pair by using maximum likelihood
estimation method where the likelihood function is derived from Poisson
statistics of neural spiking. The universal approximation feature of the
recurrent dynamical neuron network models allow us to describe
excitatory-inhibitory characteristics of an actual sensory neural network with
any desired number of neurons. The stimulus data is generated by a Phased
Cosine Fourier series having fixed amplitude and frequency but a randomly shot
phase. Various values of amplitude, stimulus component size and sample size are
applied in order to examine the effect of stimulus to the identification
process. Results are presented in tabular form at the end of this text.
