Modeling Short Over-Dispersed Spike-Train Data: A Hierarchical Parametric Empirical Bayes Framework

In this letter, a Hierarchical Parametric Empirical Bayes (HPEB) model is proposed to fit spike count data. We have integrated Generalized Linear Models and empirical Bayes theory to simultaneously solve three problems: (1) over-dispersion of spike count values; (2) biased estimation of the maximum likelihood method and (3) difficulty in sampling from high-dimensional data with fully Bayes estimators. We apply the model to study both simulated data and experimental neural data from the retina. The simulation results indicate that the new model can estimate both the weights of connections among neural populations and the output firing rates efficiently and accurately. The results from the retinal datasets show that the proposed model outperforms both standard Poisson and Negative Binomial Generalized Linear Models in terms of the prediction log-likelihood of held-out datasets.