On the parameter estimation for diffusion models of single neuron's activities

 For the Ornstein-Uhlenbeck neuronal model a quantitative method is proposed for the estimation of the two parameters characterizing the unkown input process, namely the neuron’s mean input per unit time μ and the infinitesimal standard deviation per unit time σ. This method is based on the experimentally observed first- and second-order moments of interspike intervals. The dependence of the estimates μ^ and σ^ on the moments of the observed interspike intervals and on the neuronal parameters is clarified, and a comparison is made between the estimates based on the classical Wiener model and those yielded by the Ornstein-Uhlenbeck model. Comprehensive tables are included in which the displayed values of μ^ and σ^ have been calculated in terms of physiologically realistic pairs of first- and second-order moments. Our method is finally applied to interspike interval data recorded from neurons in the mesencephalic reticular formation of the cat during hypothetical sleep, slow-wave sleep stage, and wake stage. Received: 10 October 1994/Accepted in revised form: 21 March 1995