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Nonparametric estimation of characteristics of the interspike interval distribution

BMC Neuroscience201516 (Suppl 1) :P131

https://doi.org/10.1186/1471-2202-16-S1-P131

  • Published:

Keywords

  • Probability Density Function
  • Kernel Function
  • Kernel Density
  • Fisher Information
  • Density Estimator

We address the problem of non-parametric estimation of the probability density function as a description of the probability distribution of noncorrelated interspike intervals (ISI) in records of neuronal activity. We also continue our previous effort [1, 2] to propose alternative estimators of the variability measures. Kernel density estimators are probably the most frequently used non-parametric estimators of the probability distribution. However, there are also other non-parametric approaches. We focus on non-parametric methods based on a principle of extrema of the Fisher information. Specifically, we focus on the maximum penalized likelihood estimation of the probability density function proposed by Good and Gaskins [3], which can be understood as a kernel estimator with a particular kernel function [4]. Other non-parametric approach we would like to address is the spline interpolation proposed by Huber [5] which can uniquely estimate the ISI distribution.

Declarations

Acknowledgements

This work was supported by the Czech Science Foundation (GACR) grants 15-06991S (Ondrej Pokora) and 15-08066S (Lubomir Kostal).

Authors’ Affiliations

(1)
Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Brno, Czech Republic
(2)
Institute of Physiology, Academy of Sciences of the Czech Republic, Prague, Czech Republic

References

  1. Kostal L, Lansky P, Pokora O: Variability measures of positive random variables. PLoS ONE. 2011, 6: e21998-PubMedPubMed CentralView ArticleGoogle Scholar
  2. Kostal L, Pokora O: Nonparametric Estimation of Information-Based Measures of Statistical Dispersion. Entropy. 2012, 14: 1221-1233.View ArticleGoogle Scholar
  3. Good IJ, Gaskins RA: Nonparametric roughness penalties for probability densities. Biometrika. 1971, 58: 255-277.View ArticleGoogle Scholar
  4. Eggermont PPB, LaRiccia VN: Maximum Penalized Likelihood Estimation: Volume I: Density Estimation. Springer. 2001Google Scholar
  5. Huber PJ: Fisher information and spline interpolation. Ann. Stat. 1974, 2: 1029-1033.View ArticleGoogle Scholar

Copyright

© Pokora and Kostal 2015

This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.

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