The extent to which groups of neurons exhibit higher-order correlations in their spiking activity is a controversial issue in current brain research. A major difficulty is that currently available tools for the analysis of massively parallel spike trains (N >10) for higher-order correlations typically require vast sample sizes. While multiple single-cell recordings become increasingly available, experimental approaches to investigate the role of higher-order correlations suffer from the limitations of available analysis techniques. We have recently presented a novel method for cumulant-based inference of higher-order correlations (CuBIC) that detects correlations of higher order even from relatively short data stretches of length T = 10–100 s. CuBIC employs the compound Poisson process (CPP) as a statistical model for the population spike counts, and assumes spike trains to be stationary in the analyzed data stretch. In the present study, we describe a non-stationary version of the CPP by decoupling the correlation structure from the spiking intensity of the population. This allows us to adapt CuBIC to time-varying firing rates. Numerical simulations reveal that the adaptation corrects for false positive inference of correlations in data with pure rate co-variation, while allowing for temporal variations of the firing rates has a surprisingly small effect on CuBICs sensitivity for correlations.
Keywords: multiple unit activity, higher-order correlations, non-stationarity, statistical population model
Citation: Staude B, Grün S and Rotter S (2010) Higher-order correlations in non-stationary parallel spike trains: statistical modeling and inference. Front. Comput. Neurosci. 4:16. doi: 10.3389/fncom.2010.00016
Received: 02 December 2009;
Paper pending published: 25 December 2009;
Accepted: 11 May 2010; Published online: 02 July 2010
Edited by:Jakob H. Macke, Max Planck Institute for Biological Cybernetics, Germany
Reviewed by:Yasser Roudi, NORDITA, Sweden Don H. Johnson, Rice University, USA
Copyright: © 2010 Staude, Grün and Rotter. This is an open-access article subject to an exclusive license agreement between the authors and the Frontiers Research Foundation, which permits unrestricted use, distribution, and reproduction in any medium, provided the original authors and source are credited.
*Correspondence: Stefan Rotter, Bernstein Center Freiburg and Faculty of Biology, Albert-Ludwig University, Hansastrasse 9a, 79104 Freiburg, Germany. e-mail: firstname.lastname@example.org