Parameter estimation of the threshold time function in the neural system

An algorithm for parameter estimation is presented for the neural system model. Because of its firing mechanism analogous to that of the model based on the first time crossing problem, this problem is solved numerically for our model according to the results of Kostyukov et al. (1981). We propose the algorithm that estimates the parameters of the model considering the equivalence between the probability density function of the 1st crossing time and that of the interspike interval, which is derived from the interspike interval histogram by making use of the spline function technique. The ability of the algorithm is ensured by the application to the simulated interspike interval data. The parameter estimation is carried out also for the practical neural data recorded in the cat's optic tract fibers in both the spontaneous and the stimulated cases. These applications will show the effectiveness of the algorithm in practical cases.