Inference for stochastic neuronal models
Stochastic models are developed to study the subthreshold behavior of the membrane potential of neurons. First, the membrane potential is modeled as a solution of stochastic differential equations driven by various stochastic processes such as Poisson processes, Wiener processes, and a mixture of Poisson and Wiener processes. Maximum-likelihood estimates of the parameters of a diffusion neuronal model are obtained. Then, the authors propose a diffusion neuronal model with time-dependent parameters and a semimartingale neuronal model which extends previously discussed models. The method of optimal estimating functions is applied in this case. A simulation study is conducted to evaluate the performance of the maximum-likelihood estimators for a diffusion neuronal model. For long periods of observation, the estimates of parameters deteriorate as the number of observed trajectories increases. This counter-intuitive phenomenon may require further investigation.
scientific article; zbMATH DE number 4195760
scientific article