Electronic Journal of Statistics

Decomposition of neuronal assembly activity via empirical de-Poissonization

Werner Ehm, Benjamin Staude, and Stefan Rotter

Full-text: Open access

Abstract

Consider a compound Poisson process with jump measure ν supported by finitely many positive integers. We propose a method for estimating ν from a single, equidistantly sampled trajectory and develop associated statistical procedures. The problem is motivated by the question whether nerve cells in the brain exhibit higher-order interactions in their firing patterns. According to the neuronal assembly hypothesis (Hebb [13]), synchronization of action potentials across neurons of different groups is considered a signature of assembly activity, but it was found notoriously difficult to demonstrate it in recordings of neuronal activity. Our approach based on a compound Poisson model allows to detect the presence of joint spike events of any order using only population spike count samples, thus bypassing both the “curse of dimensionality” and the need to isolate single-neuron spike trains in population signals.

Article information

Source
Electron. J. Statist., Volume 1 (2007), 473-495.

Dates
First available in Project Euclid: 14 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1195051631

Digital Object Identifier
doi:10.1214/07-EJS095

Mathematical Reviews number (MathSciNet)
MR2357714

Zentralblatt MATH identifier
1320.62069

Subjects
Primary: 62G05: Estimation 62E20: Asymptotic distribution theory 92C20: Neural biology

Keywords
asymptotics compound Poisson process empirical characteristic function higher-order interactions jump measure spike train synchronized activity

Citation

Ehm, Werner; Staude, Benjamin; Rotter, Stefan. Decomposition of neuronal assembly activity via empirical de-Poissonization. Electron. J. Statist. 1 (2007), 473--495. doi:10.1214/07-EJS095. https://projecteuclid.org/euclid.ejs/1195051631


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