Fitting a stochastic spiking model to neuronal current injection data

Spiking neuron models have advanced to the stage of accurately predicting the spike times of individual biological neurons for given fluctuating current. Most of the successful models are based on deterministic mechanistic modeling. In order to describe the stochastic aspect of neuronal firing, I propose setting a deterministic model in a stochastic framework, namely, incorporating the multi-timescale adaptive threshold (MAT) model of neuronal spiking into the stochastic framework of the linear–nonlinear Poisson (LNP) model in the form of a generalized linear model (GLM). In this setting, the probability of spike occurrence is updated each time a spike is derived from the past probability. Accordingly, the model may account for nontrivial firing patterns of various neurons that cannot be realized with the inhomogeneous Poisson process. The stochastic MAT model is not only capable of characterizing firing mechanisms specific to individual neurons, but may render the statistical inference feasible for the underlying mechanisms from the data. I also examine here two plausible principles for adjusting the model parameters: maximizing the spike time coincidence between the model and data, and maximizing the likelihood. It is found that these principles bring about greatly different characteristics for an identical set of data.