Significance of joint-spike events based on trial-shuffling by efficient combinatorial methods

The assembly hypothesis suggests that information processing in the cortex is mediated by groups of neurons expressed by their coordinated spiking activity. Thus, the unitary events analysis was designed to detect the presence of conspicuous joint-spike events in multiple single-unit recordings and to evaluate their statistical significance. The null hypothesis of the associated test assumes independent Poisson processes and leads to parametric significance estimation. In order to allow for arbitrary processes here we suggest to base the significance estimation on trial shuffling and resampling. In this scheme the null hypothesis is implemented by combining spike trains from nonsimultaneous trials and counting the joint-spike events. The coincidence distribution serving for the significance estimation is generated by repetitive resampling. The number of all possible recombinations, however, grows dramatically with the number of trials and neurons and thus is not practical for a user-interactive implementation of the analysis. We have suggested a Monte-Carlo-based resampling procedure and demonstrated that the procedure yields an appropriate estimate of the distribution and reliable significance estimation. In contrast, here, we present an exact solution. Rewriting the statistical problem in terms of certain macrostates, we are able to systematically sample the coincidence counts from all trial combinations. In addition we restrict the generating process to those counts forming the relevant tail of the distribution. The computationally effective implementation uses the concept of partitions. © 2003 Wiley Periodicals, Inc.