Decomposition of neuronal assembly activity via empirical de-Poissonization

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 (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.