Quantifying statistical interdependence, part III: N > 2 point processes

Stochastic event synchrony (SES) is a recently proposed family of similarity measures. First, "events" are extracted from the given signals; next, one tries to align events across the different time series. The better the alignment, the more similar the N time series are considered to be. The similarity measures quantify the reliability of the events (the fraction of "nonaligned" events) and the timing precision. So far, SES has been developed for pairs of one-dimensional (Part I) and multidimensional (Part II) point processes. In this letter (Part III), SES is extended from pairs of signals to N > 2 signals. The alignment and SES parameters are again determined through statistical inference, more specifically, by alternating two steps: (1) estimating the SES parameters from a given alignment and (2), with the resulting estimates, refining the alignment. The SES parameters are computed by maximum a posteriori (MAP) estimation (step 1), in analogy to the pairwise case. The alignment (step 2) is solved by linear integer programming. In order to test the robustness and reliability of the proposed N-variate SES method, it is first applied to synthetic data. We show that N-variate SES results in more reliable estimates than bivariate SES. Next N-variate SES is applied to two problems in neuroscience: to quantify the firing reliability of Morris-Lecar neurons and to detect anomalies in EEG synchrony of patients with mild cognitive impairment. Those problems were also considered in Parts I and II, respectively. In both cases, the N-variate SES approach yields a more detailed analysis.