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Mathematical Biosciences and Engineering

2014, Volume 11, Issue 1: 105-123. doi: 10.3934/mbe.2014.11.105
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Fano factor estimation

  • 1.
    Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Kotlarska 2a, 611 37 Brno
  • 2.
    Institute of Physiology, Academy of Sciences of the Czech Republic, Videnska 1083, 142 20 Prague
  • Received: 01 December 2012 Accepted: 29 June 2018 Published: 01 September 2013

  • MSC : Primary: 60K05, 62-07; Secondary: 62P10.

  • Fano factor is one of the most widely used measures ofvariability of spike trains. Its standard estimator is the ratio of samplevariance to sample mean of spike counts observed in a time window and thequality of the estimator strongly depends on the length of the window. Weinvestigate this dependence under the assumption that the spike trainbehaves as an equilibrium renewal process. It is shown whatcharacteristics of the spike train have large effect on the estimatorbias. Namely, the effect of refractory period is analytically evaluated.Next, we create an approximate asymptotic formula for the mean squareerror of the estimator, which can also be used to find minimum of theerror in estimation from single spike trains. The accuracy of the Fano factorestimator is compared with the accuracy of the estimator based on the squaredcoefficient of variation. All the results are illustrated for spike trainswith gamma and inverseGaussian probability distributions of interspike intervals. Finally, wediscuss possibilities of how to select a suitable observation window for the Fanofactor estimation.

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

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  • Fano factor is one of the most widely used measures ofvariability of spike trains. Its standard estimator is the ratio of samplevariance to sample mean of spike counts observed in a time window and thequality of the estimator strongly depends on the length of the window. Weinvestigate this dependence under the assumption that the spike trainbehaves as an equilibrium renewal process. It is shown whatcharacteristics of the spike train have large effect on the estimatorbias. Namely, the effect of refractory period is analytically evaluated.Next, we create an approximate asymptotic formula for the mean squareerror of the estimator, which can also be used to find minimum of theerror in estimation from single spike trains. The accuracy of the Fano factorestimator is compared with the accuracy of the estimator based on the squaredcoefficient of variation. All the results are illustrated for spike trainswith gamma and inverseGaussian probability distributions of interspike intervals. Finally, wediscuss possibilities of how to select a suitable observation window for the Fanofactor estimation.


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    8. Kamil Rajdl, Petr Lansky, Lubomir Kostal, Fano Factor: A Potentially Useful Information, 2020, 14, 1662-5188, 10.3389/fncom.2020.569049
    9. Romi Mankin, Astrid Rekker, Sander Paekivi, Statistical moments of the interspike intervals for a neuron model driven by trichotomous noise, 2021, 103, 2470-0045, 10.1103/PhysRevE.103.062201
    10. Rimjhim Tomar, Lubomir Kostal, Variability and Randomness of the Instantaneous Firing Rate, 2021, 15, 1662-5188, 10.3389/fncom.2021.620410
    11. Adam J. Peterson, Dexter R.F. Irvine, Peter Heil, A Model of Synaptic Vesicle-Pool Depletion and Replenishment Can Account for the Interspike Interval Distributions and Nonrenewal Properties of Spontaneous Spike Trains of Auditory-Nerve Fibers, 2014, 34, 0270-6474, 15097, 10.1523/JNEUROSCI.0903-14.2014
    12. A. Rekker, S. Paekivi, R. Mankin, 2022, 2522, 0094-243X, 070004, 10.1063/5.0100761
    13. Ankan Chandra, G K Singh, Vinay Pant, 2023, Empirical Wavelet Transform and Fano Equality Ratio Test-based Fault Detection Scheme for Inverter Dominated Autonomous Microgrid, 978-1-6654-7517-4, 1, 10.1109/ICONAT57137.2023.10080580
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