Quantifying variability in neural responses and its application for the validation of model predictions

A rate code assumes that a neuron's response is completely characterized by its time-varying mean firing rate. This assumption has successfully described neural responses in many systems. The noise in rate coding neurons can be quantified by the coherence function or the correlation coefficient between the neuron's deterministic time-varying mean rate and noise corrupted single spike trains. Because of the finite data size, the mean rate cannot be known exactly and must be approximated. We introduce novel unbiased estimators for the measures of coherence and correlation which are based on the extrapolation of the signal to noise ratio in the neural response to infinite data size. We then describe the application of these estimates to the validation of the class of stimulus-response models that assume that the mean firing rate captures all the information embedded in the neural response. We explain how these quantifiers can be used to separate response prediction errors that are due to inaccurate model assumptions from errors due to noise inherent in neuronal spike trains.