-
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
-
Abstract
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.
References
|
[1]
|
Exp. Brain Res., 210 (2011), 353-371.
|
|
[2]
|
J. Neurosci., 21 (2001), 5328-5343.
|
|
[3]
|
J. Neurosci. Methods, 32 (2012), 2204-2216.
|
|
[4]
|
Nat. Neurosci., 13 (2010), 369-378.
|
|
[5]
|
Methuen & Co., Ltd., London; John Wiley & Sons, Inc., New York, 1962.
|
|
[6]
|
Brain Res., 1118 (2006), 84-93.
|
|
[7]
|
J. Comput. Neurosci., 32 (2012), 443-463.
|
|
[8]
|
Neural. Comput., 23 (2011), 1944-1966.
|
|
[9]
|
J. Neurosci. Methods, 190 (2010), 149-152.
|
|
[10]
|
Phys. Rev. E, 79 (2009), 021905.
|
|
[11]
|
Cambridge University Press, Cambridge, 2002.
|
|
[12]
|
P. Natl. Acad. Sci. USA, 107 (2010), 21842-21847.
|
|
[13]
|
Oper. Res., 8 (1960), 446-472.
|
|
[14]
|
PLOS ONE, 6 (2011), e21998.
|
|
[15]
|
BioSystems, 89 (2007), 69-73.
|
|
[16]
|
McGraw-Hill, Inc., 1974.
|
|
[17]
|
in "Analysis of Parallel Spike Trains," Springer, Inc., New York, (2010), 37-58.
|
|
[18]
|
J. Neurosci. Methods, 169 (2008), 374-390.
|
|
[19]
|
Neural. Comput., 23 (2011), 3125-3144.
|
|
[20]
|
Neural. Comput., 20 (2008), 1325-1343.
|
|
[21]
|
Cambridge University Press, Cambridge, 1950.
|
|
[22]
|
J. Comput. Neurosci., 29 (2010), 351-365.
|
|
[23]
|
Neural. Comput., 21 (2009), 1931-1951.
|
|
[24]
|
BioSystems, 79 (2005), 67-72.
|
|
[25]
|
Hearing Res., 46 (1990), 41-52.
|
-
-
-
-
DownLoad: