Probabilistic models for determining the input-output relationship in formalized neurons. I. A theoretical approach

In order to investigate under which assumptions one can expect to determine the probabilistic response of a neural unit to an incoming stochastic excitation, we propose a model that endows the neuron with a variable threshold. It is shown that a fairly complete statistical description of the input-output relationships can be obtained when the input is Poisson, non-homogeneous Poisson and, finally, any stationary continuous stochastic process.