State space method for predicting the spike times of a neuron

It has been established that a biological neuron reproduces the precise spike response to identical fluctuating input currents. We wish to predict the firing times of a given neuron for any input current. For this purpose, a mathematical model is introduced for mimicking the voltage response of the neuron to an input current. In predicting the firing times of a target neuron for a novel input current, we propose here the method of estimating the probability of spike occurrence, instead of naively thresholding an instantaneous value of the model voltage. The assessment is carried out maximally utilizing the information about the state space of the voltage and its time derivative(s) of the model, in advance of a possible spike, with a time lag that is determined by maximizing the mutual information. The prediction is significantly improved by the present method in comparison to the naive thresholding method.