Fano factor estimation
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 dependenc...
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AIMS Press
2013-08-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.105 |
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| author | Kamil Rajdl Petr Lansky |
| author_facet | Kamil Rajdl Petr Lansky |
| author_sort | Kamil Rajdl |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-7d7759d8e90d40ebb9ce4fcf97a43575 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2013-08-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-7d7759d8e90d40ebb9ce4fcf97a435752025-01-24T02:26:48ZengAIMS PressMathematical Biosciences and Engineering1551-00182013-08-0111110512310.3934/mbe.2014.11.105Fano factor estimationKamil Rajdl0Petr Lansky1Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Kotlarska 2a, 611 37 BrnoInstitute of Physiology, Academy of Sciences of the Czech Republic, Videnska 1083, 142 20 PragueFano 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.https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.105renewal processfano factorrefractory period.mean square errorestimation |
| spellingShingle | Kamil Rajdl Petr Lansky Fano factor estimation Mathematical Biosciences and Engineering renewal process fano factor refractory period. mean square error estimation |
| title | Fano factor estimation |
| title_full | Fano factor estimation |
| title_fullStr | Fano factor estimation |
| title_full_unstemmed | Fano factor estimation |
| title_short | Fano factor estimation |
| title_sort | fano factor estimation |
| topic | renewal process fano factor refractory period. mean square error estimation |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.105 |
| work_keys_str_mv | AT kamilrajdl fanofactorestimation AT petrlansky fanofactorestimation |