Identification of a stochastic resonate-and-fire neuronal model via nonlinear least squares and maximum likelihood estimation

Recent work has shown that the resonate-and-fire neuronal model is both computationally efficient and suitable for large network simulations. In this paper, we examine the estimation problem of a resonate-and-fire neuronal model with stochastic firing threshold. The model parameters are divided into two sets. The first set is associated with the subthreshold behaviour and can be estimated by a least squares algorithm, while the second set includes parameters associated with the firing threshold and its identification is formulated as a maximum likelihood estimation problem. The latter is in turn solved by a simulated annealing approach that avoids local optima. The proposed identification approach is evaluated using both simulated and in-vitro data, which shows a good match between prediction by identified model and the actual data, concluding the efficiency and accuracy of the proposed approach.