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