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Mathematical Biosciences and Engineering

2014, Volume 11, Issue 1: 63-80. doi: 10.3934/mbe.2014.11.63
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The effect of interspike interval statistics on the information gainunder the rate coding hypothesis

  • 1.
    The Institute of Statistical Mathematics, 10-3 Midori-cho, Tachikawa, Tokyo 190-8562
  • 2.
    Institute of Physiology, Academy of Sciences of the Czech Republic, Videnska 1083, 14220 Prague
  • Received: 01 December 2012 Accepted: 29 June 2018 Published: 01 September 2013

  • MSC : Primary: 60G55, 62P10; Secondary: 94A17.

  • The question, how much information can be theoreticallygained from variable neuronal firing rate with respect to constantaverage firing rate is investigated.We employ the statistical concept of information based on the Kullback-Leibler divergence,and assume rate-modulated renewal processes as a model of spike trains.We show thatif the firing rate variation is sufficiently small and slow(with respect to the mean interspike interval), the information gaincan be expressed by the Fisher information.Furthermore, under certain assumptions, the smallestpossible information gain is provided by gamma-distributed interspikeintervals.The methodology is illustrated and discussed on severaldifferent statistical models of neuronal activity.

    Citation: Shinsuke Koyama, Lubomir Kostal. The effect of interspike interval statistics on the information gainunder the rate coding hypothesis[J]. Mathematical Biosciences and Engineering, 2014, 11(1): 63-80. doi: 10.3934/mbe.2014.11.63

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  • The question, how much information can be theoreticallygained from variable neuronal firing rate with respect to constantaverage firing rate is investigated.We employ the statistical concept of information based on the Kullback-Leibler divergence,and assume rate-modulated renewal processes as a model of spike trains.We show thatif the firing rate variation is sufficiently small and slow(with respect to the mean interspike interval), the information gaincan be expressed by the Fisher information.Furthermore, under certain assumptions, the smallestpossible information gain is provided by gamma-distributed interspikeintervals.The methodology is illustrated and discussed on severaldifferent statistical models of neuronal activity.


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