A self exciting point process model for neural spike sequences, and its rate estimation

Common neuron firing rate estimators have been criticized because of their Poisson assumption, not accounting for the refractory period of action potentials that induces history dependency in spike sequences. Hence rate estimators that can account for such dependency, although seemingly more difficult to formulate, could provide more accurate results. In this paper a Maximum Likelihood (ML) estimator for an inhomogeneous Poisson process is modified to account for an absolute refractory period in the spike sequence. The proposed estimator treats the refractory period as a nuisance parameter and maximizes the profile likelihood of the stimulus. Through computer simulations we show that by exploiting the refractory phenomenon, the estimator can achieve better performance than the Poisson estimator for moderate to high firing rates. Furthermore, we show that the results provided by this estimator yield an improved goodness of fit to real data when compared to the Poisson estimator.