The estimation of interspike interval (ISI) distributions from experimental data is a common method to study neuronal variability given a certain stationary input. In a typical experiment, the spike train of a single neuron (e.g., a neuron in visual cortex) is recorded while driven by a constant stimulus. The stimulus might be an external input applied to the system (e.g., a visual contrast grating moving at constant speed); or it may be an intracellularly applied constant driving current. The spike train is analyzed and the distribution of intervals between two subsequent spikes is plotted in a histogram. For a sufficiently long spike train, the histogram provides a good estimate of the ISI distribution which we denote as ; cf. Fig. 7.9. The interval distribution can be interpreted as a conditional probability density
where is the probability that the next spike occurs in the interval given that the last spike occurred at time .
In order to extract the mean firing rate from a stationary interval distribution , we start with the definition of the mean interval,
The mean firing rate is the inverse of the mean interval
Interspike interval distributions derived from a spike train under stationary conditions can be broad or sharply peaked. To quantify the width of the interval distribution, neuroscientists often evaluate the coefficient of variation, short , defined as the ratio of the standard deviation and the mean. Therefore the square of the is
where and . A Poisson process produces distributions with . A value of , implies that a given spike train is less regular than a Poisson process with the same firing rate. If , then the spike train is more regular. Most deterministic integrate-and-fire neurons fire periodically when driven by a constant stimulus and therefore have . Intrinsically bursting neurons, however, can have .
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