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

In this letter, a Hierarchical Parametric Empirical Bayes model is proposed to model spike count data. We have integrated Generalized Linear Models (GLMs) and empirical Bayes theory to simultaneously provide three advantages: (1) a model of over-dispersion of spike count values; (2) reduced MSE in estimation when compared to using the maximum likelihood method for GLMs; and (3) an efficient alternative to inference 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 (mean spike count) efficiently and accurately. The results from the retinal datasets show that the proposed model outperforms both standard Poisson and Negative Binomial GLMs in terms of the prediction log-likelihood of held-out datasets.