Quantifying reliability of spiking rate estimation

The CV was used to quantify the reliability of a neuron’s spiking activity. Due to the trial-to-trial variability of neural responses, the number of spikes a neuron fires in a time window varies across repetitive tests. The spiking rate derived from the spike count is thus a random variable. CV is the ratio of the standard deviation over the mean for this spiking rate estimate. It measures the absolute variability of the spiking rate relative to its true magnitude, thus offering a quantification more closely related to the informational capacity of the neural activity than the absolute variability value. In reality, the standard deviation and the mean of the spiking rate estimate are calculated from the repetitively tested trials. For Poisson neurons, the CV and the true spiking rate have a fixed relationship given a fixed window length. To examine the relationship between these 2 values in real neural data, the mean spiking rate was used as an estimate of the true rate. CV and the mean spiking rate were calculated for each neuron and stimulus pair in 15-ms nonoverlapping windows. The relationship between the CV and the mean spiking rate was then compared to that of Poisson neurons (Fig 6B). To quantify how the observed relationship approaches that of Poisson-spiking neurons, the coefficient of determination (r²) between theoretical CV values CV_Poisson(i) and observed CV values CV_obs(i) was calculated. CV_Poisson(i) was calculated by Eq 9 as derived in S1 Text, in which r_m(i) is the corresponding mean spiking rate:

The mean of the observed CV value was then calculated by Eq 10. The coefficient of determination then assessed the amount of explained variance in the data set (Eq 11).