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Analysis of Neural Data

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A Frank Mixture Copula Family for Modeling Higher-Order Correlations of Neural Spike Counts
Citation key Onken2009a
Author Onken, A. and Obermayer, K.
Title of Book Journal of Physics: Conference Series
Year 2009
DOI http://dx.doi.org/10.1088/1742-6596/197/1/012019
Journal Journal of Physics: Conference Series
Volume 197
Publisher IOP
Abstract In order to evaluate the importance of higher-order correlations in neural spike count codes, flexible statistical models of dependent multivariate spike counts are required. Copula families, parametric multivariate distributions that represent dependencies, can be applied to construct such models. We introduce the Frank mixture family as a new copula family that has separate parameters for all pairwise and higher-order correlations. In contrast to the Farlie-Gumbel-Morgenstern copula family that shares this property, the Frank mixture copula can model strong correlations. We apply spike count models based on the Frank mixture copula to data generated by a network of leaky integrate-and-fire neurons and compare the goodness of fit to distributions based on the Farlie-Gumbel-Morgenstern family. Finally, we evaluate the importance of using proper single neuron spike count distributions on the Shannon information. We find notable deviations in the entropy that increase with decreasing firing rates. Moreover, we find that the Frank mixture family increases the log likelihood of the fit significantly compared to the Farlie-Gumbel-Morgenstern family. This shows that the Frank mixture copula is a useful tool to assess the importance of higher-order correlations in spike count codes.
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