Testing the Odds of Inherent versus Observed Over-dispersion

25 The repeated presentation of an identical visual stimulus in the receptive field of a neuron may evoke 26 different spiking patterns at each trial. Probabilistic methods are essential to understand the functional 27 role of this variance within the neural activity. In that case, a Poisson process is the most common model 28 of trial-to-trial variability. For a Poisson process, the variance of the spike count is constrained to be 29 equal to the mean, irrespective of the duration of measurements. Numerous studies have shown that this 30 relationship does not generally hold. Specifically, a majority of electrophysiological recordings show an 31 “over-dispersion” effect: Responses that exhibit more inter-trial variability than expected from a Poisson 32 process alone. A model that is particularly well suited to quantify over-dispersion is the Negative-Binomial 33 distribution model. This model is well-studied and widely used but has only recently been applied to 34 neuroscience. In this paper, we address three main issues. First, we describe how the Negative-Binomial 35 distribution provides a model apt to account for overdispersed spike counts. Second, we quantify the 36 significance of this model for any neurophysiological data by proposing a statistical test, which quantifies 37 the odds that over-dispersion could be due to the limited number of repetitions (trials). We apply this 38 test to three neurophysiological tests along the visual pathway. Finally, we compare the performance of 39 this model to the Poisson model on a population decoding task. We show that the decoding accuracy is 40 improved when accounting for over-dispersion, especially under the hypothesis of tuned over-dispersion. 41