Realistic Spiking Neuron Statistics in a Population are Described by a Single Parametric Distribution

Abstract

The spiking of activity of neurons throughout the cortex is random and complicated. This complicated activity requires theoretical formulations in order to understand the underlying principles of neural processing. A key aspect of theoretical investigations is characterizing the probability distribution of spiking activity. This study aims to better understand the statistics of the time between spikes, or interspike interval, in both real data and a spiking model with many time scales. Exploration of the interspike intervals of neural network activity can provide a better understanding of neural responses to different stimuli. We consider different parametric distribution fitting techniques to characterize the random spike times of a population of neurons in the visual cortex of a mammal. Five different probability distribution functions were considered, including three mixture models, and their goodness of fit was determined through two criteria: maximum likelihood and Akaike Information Criteria. Despite being largely heterogeneous, both criteria indicated that one distribution, although different for each criteria, was the best fitting for all of the neurons in the data set. The Gamma-Gamma mixture distribution was the best according to maximum likelihood and the Exponential distribution was the best according to AIC. The statistical methodology applied to a burst model yielded the same results, and the AIC formula was further investigated to better understand its consistent selection of the same parametric distribution. We find that complicated neural spiking activity can sometimes be described by a single parametric distribution, which is hopefully comforting for theorists.