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Center for Nonlinear Studies |
The Ornstein-Uhlenbeck process has been proposed as a odel for the spontaneous/stochastic activity of a single neuron. In this model, the firing of the neuron corresponds to the first-passage time of the process to a constant boundary, or threshold. In this talk, the governing Ornstein-Uhlenbeck process is derived from basic physical assumptions. Then, the problem of estimating the parameters of the process is addressed when the only available data from a neuron are the interspike intervals, or the times between firings. While the Laplace transform of the first-passage time density is available, the real density has not been obtained in any tractable form. This talk concludes by demonstrating a technique for obtaining a maximum likelihood estimate (MLE) of the parameters based on a numerical inversion of the Laplace Transform.