Estimation of the input parameters in the Ornstein-Uhlenbeck neuronal model.

The stochastic Ornstein-Uhlenbeck neuronal model is studied, and estimators of the model input parameters, depending on the firing regime of the process, are derived. Closed expressions for the Laplace transforms of the first two moments of the normalized first-passage time through a constant boundary in the suprathreshold regime are derived, which is used to define moment estimators. In the subthreshold regime, the exponentiality of the first-passage time is utilized to characterize the input parameters. In the threshold regime and for the Wiener process approximation, analytic expressions for the first-passage-time density are used to derive the maximum-likelihood estimators of the parameters. The methods are illustrated on simulated data under different conditions, including misspecification of the intrinsic parameters of the model. Finally, known approximations of the first-passage-time moments are improved.