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MBE

Fano factor is one of the most widely used measures of
variability of spike trains. Its standard estimator is the ratio of sample
variance to sample mean of spike counts observed in a time window and the
quality of the estimator strongly depends on the length of the window. We
investigate this dependence under the assumption that the spike train
behaves as an equilibrium renewal process. It is shown what
characteristics of the spike train have large effect on the estimator
bias. Namely, the effect of refractory period is analytically evaluated.
Next, we create an approximate asymptotic formula for the mean square
error of the estimator, which can also be used to find minimum of the
error in estimation from single spike trains. The accuracy of the Fano factor
estimator is compared with the accuracy of the estimator based on the squared
coefficient of variation. All the results are illustrated for spike trains
with gamma and inverse
Gaussian probability distributions of interspike intervals. Finally, we
discuss possibilities of how to select a suitable observation window for the Fano
factor estimation.

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