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Bayesian estimation of the time-varing rate and irregularity of neuronal firing


Spike trains generated by cortical neurons possess specific characteristics such as firing irregularity (see Figure 1A) other than the firing rate. Recently, our study revealed that the firing irregularity is rather specific to individual neurons and invariant with the time and the modulation of firing rate by using a metric for analyzing the time-local irregularity of spike events [1, 2]. On the other hand, it was also reported that the firing irregularity varied significantly according to behavioral contexts in some other cortical area [3]. Therefore, we wish to examine how easily the firing irregularity is varied with the firing rate more systematically. For this purpose, we developed a Bayesian estimation method that allows us to estimate both the instantaneous rate and irregularity for a given spike sequence [4]. In our new framework, we first consider the stochastic process of generating spikes under a given rate and irregularity, and then invert the conditional probability distribution to infer the rate and the irregularity from the data.

Figure 1
figure 1

(A) Sample sequences of events with identical rate and different irregularity, which may be termed bursty, random (Poisson), or regular. (B) The MAP estimate of the instantaneous rate λ(t) and irregularity κ(t) for the spike sequence {ti} recorded from a V1 neuron of a Macaque (nsa2004.4; Neural Signal Archive [5]).

We applied our new method to the experimentally recorded spike data taken from Neural Signal Archive [5] (see Figure 1B), and revealed that there is a systematic correlation between firing rate and firing irregularity, and that the degree of the variability in the firing irregularity greatly depends on the cortical areas.


  1. Shinomoto S, Shima K, Tanji J: Differences in spiking patterns among cortical neurons. Neural Comput. 2003, 15: 2823-2842. 10.1162/089976603322518759.

    Article  PubMed  Google Scholar 

  2. Shinomoto S, Miyazaki Y, Tamura H, Fujita I: Regional and laminar differences in in vivo firing patterns of primate cortical neurons. J Neurophysiol. 2005, 94: 567-575. 10.1152/jn.00896.2004.

    Article  PubMed  Google Scholar 

  3. Davies RM, Gerstein GL, Baker SN: Measurement of time-dependent changes in the irregularity of neural spiking. J Neurophysiol. 2006, 96: 906-918. 10.1152/jn.01030.2005.

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  4. Shimokawa T, Shinomoto S: Estimating instantaneous irregularity of neuronal firing. Neural Comput. 2009,

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  5. Neural Signal Archive. []

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This study was supported in part by Grants-in-Aid for Scientific Research to SS from the MEXT Japan. TS is supported by the Research Fellowship of the JSPS for Young Scientists.

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Correspondence to Takeaki Shimokawa.

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Open Access This article is published under license to BioMed Central Ltd. This is an Open Access article is distributed under the terms of the Creative Commons Attribution 2.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Shimokawa, T., Shinomoto, S. Bayesian estimation of the time-varing rate and irregularity of neuronal firing. BMC Neurosci 10 (Suppl 1), O6 (2009).

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