Neural noise sets a limit to information transmission in sensory systems. In several areas, the spiking response (to a repeated stimulus) has shown a higher degree of regularity than predicted by a Poisson process. However, a simple model to explain this low variability is still lacking. Here we introduce a new model, with a correction to Poisson statistics, that can accurately predict the regularity of neural spike trains in response to a repeated stimulus. The model has only two parameters but can reproduce the observed variability in retinal recordings in various conditions. We show analytically why this approximation can work. In a model of the spike-emitting process where a refractory period is assumed, we derive that our simple correction can well approximate the spike train statistics over a broad range of firing rates. Our model can be easily plugged to stimulus processing models, like a linear-nonlinear model or its generalizations, to replace the Poisson spike train hypothesis that is commonly assumed. It estimates the amount of information transmitted much more accurately than Poisson models in retinal recordings. Thanks to its simplicity, this model has the potential to explain low variability in other areas.

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