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Decomposition of neuronal assembly activity via empirical de-Poissonization. (English) Zbl 1320.62069

Summary: Consider a compound Poisson process with jump measure \(\nu\) supported by finitely many positive integers. We propose a method for estimating \(\nu\) 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 [D. O. Hebb, The organization of behavior: a neuropsychological theory. New York: Wiley (1949)], 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 difficulties of simultaneously recording the spike trains of many single units.

MSC:

62G05 Nonparametric estimation
62E20 Asymptotic distribution theory in statistics
92C20 Neural biology
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