Maximum Likelihood Estimation of an Integrate and Fire Neuronal Model
The Ornstein Uhlenbeck process has been proposed as a model for the spontaneous activity of a neuron. In this model, the firing of the neuron corresponds to the first passage of the process to a constant boundary, or threshold. While the Laplace transform of the first passage time distribution is available, the probability distribution function has not been obtained in any tractable form. We address the problem of estimating the parameters of the process when the only available data from a neuron are the interspike intervals, or the times between firings. In particular, we give an algorithm for computing maximum likelihood estimates (MLEs) and their corresponding confidence regions for the three identifiable (of the five model) parameters by numerically inverting the Laplace transform. A comparison of the two parameter algorithm (where the time constantis known a priori) to the three parameter algorithm shows that significantly more data is required in the latter case to achieve comparable parameter resolution as measured by 95% confidence intervals widths. The computational methods described here are an efficient, biophysically revealing alternative to the well known moment based estimations for OU integrate and fire (IF) models. Moreover, it could serve as a template for performing parameter inference on more complex IF neuronal models.