# American Institute of Mathematical Sciences

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2014, 11(1): 105-123. doi: 10.3934/mbe.2014.11.105

## Fano factor estimation

 1 Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Kotlarska 2a, 611 37 Brno, Czech Republic 2 Institute of Physiology, Academy of Sciences of the Czech Republic, Videnska 1083, 142 20 Prague

Received  December 2012 Revised  December 2012 Published  September 2013

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.
Citation: Kamil Rajdl, Petr Lansky. Fano factor estimation. Mathematical Biosciences & Engineering, 2014, 11 (1) : 105-123. doi: 10.3934/mbe.2014.11.105
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