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This article is part of the supplement: Twentieth Annual Computational Neuroscience Meeting: CNS*2011

Open Access Poster presentation

Detection and localization of multiple rate changes in Poisson spike trains

Marietta Tillmann1, Michael Messer1*, Markus Bingmer1, Julia Schiemann2, Ralph Neininger1, Jochen Roeper2 and Gaby Schneider1

Author Affiliations

1 Institute of Mathematics, Goethe-University Frankfurt, Germany

2 Institute of Neurophysiology, Neuroscience Center, Goethe-University Frankfurt, Germany

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BMC Neuroscience 2011, 12(Suppl 1):P268  doi:10.1186/1471-2202-12-S1-P268

The electronic version of this article is the complete one and can be found online at:

Published:18 July 2011

© 2011 Messer et al; licensee BioMed Central Ltd.

This is an open access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Poster presentation

In statistical spike train analysis, stochastic point process models usually assume stationarity, in particular that the underlying spike train shows a constant firing rate (e.g. [1]). However, such models can lead to misinterpretation of the associated tests if the assumption of rate stationarity is not met (e.g. [2]). Therefore, the analysis of nonstationary data requires that rate changes can be located as precisely as possible. However, present statistical methods focus on rejecting the null hypothesis of stationarity without explicitly locating the change point(s) (e.g. [3]).

We propose a test for stationarity of a given spike train that can also be used to estimate the change points in the firing rate. Assuming a Poisson process with piecewise constant firing rate, we propose a Step-Filter-Test (SFT) which can work simultaneously in different time scales, accounting for the high variety of firing patterns in experimental spike trains. Formally, we compare the numbers N1=N1(t,h) and N2=N2(t,h) of spikes in the time intervals (t-h,t] and (h,t+h]. By varying t within a fine time lattice and simultaneously varying the interval length h, we obtain a multivariate statistic D(h,t):=(N1-N2)/√(N1+N2), for which we prove asymptotic multivariate normality under homogeneity. From this a practical, graphical device to spot changes of the firing rate is constructed.

Our graphical representation of D(h,t) (Figure 1A) visualizes the changes in the firing rate. For the statistical test, a threshold K is chosen such that under homogeneity, |D(h,t)|<K holds for all investigated h and t with probability 0.95. This threshold can indicate potential change points in order to estimate the inhomogeneous rate profile (Figure 1B). The SFT is applied to a sample data set of spontaneous single unit activity recorded from the substantia nigra of anesthetized mice. In this data set, multiple rate changes are identified which agree closely with visual inspection. In contrast to approaches choosing one fixed kernel width [4], our method has advantages in the flexibility of h.

thumbnailFigure 1. Graphical representation of the step filter test (SFT) that detects rate changes in Poisson spike trains. A. Curves indicate values of D(h,t) as a function of time t for different window sizes h (in different colors). B. Rate histogram (grey) of the corresponding spike train. Blue step function indicates estimated rate profile.


We thank Brooks Ferebee for stimulating discussions. This work was supported by the LOEWE-Schwerpunkt “Neuronale Koordination Forschungsschwerpunkt Frankfurt” (MM, JR), by the BMBF Project Bernstein Fokus: Neurotechnologie Frankfurt, FKZ 01GQ0841 (MB) and by the Deutsche Forschungsgemeinschaft SFB 815 (JR).


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