Estimation of neuronal dynamics of Izhikevich neuron models from spike-train data with particle Markov chain Monte Carlo method

Many neuronal models reproducing electrical activities of neurons have been proposed. Among such neuronal models, the Izhikevich neuron model is known to reproduce various kinds of electrical responses with low computational cost. It is difficult, however, to determine the model parameters of neuronal models including the Izhikevich neuron model which reproduce observed data since the latent variables of the neurons, such as membrane potential and channel variables, cannot be observed directly and only one of multidimensional latent variables of neurons or only spike-train data can be observed through partial observations. In this paper, we propose a data-driven method for estimating the latent variables and the parameters of the Izhikevich neuron model from only spike-train data. In the proposed method, we estimate the joint posterior distribution of latent variables and parameters by employing the replica exchange particle-Gibbs with ancestor sampling method, in order to overcome existence of local optima in parameters due to limited observations. Furthermore, we verify the effectiveness of the proposed method by using spike-train data generated from the Izhikevich neuron model. (author)