Significance of coincident spiking considering inter-spike interval variability and serial interval correlation

Abstract

Event Abstract Back to Event Significance of coincident spiking considering inter-spike interval variability and serial interval correlation Martin P. Nawrot1, 2*, Farzad Farkhooi1, 2 and Sonja Grün2, 3 1 Freie Universität Berlin, Germany 2 BCCN Berlin, Germany 3 RIKEN Brain Science Institute, Japan It is believed that information processing in higher brain centers such as the mammalian neocortex is achieved by ensembles of neurons that concert their spiking activity. To test whether spike patterns expressed as spike synchrony are present in experimental data statistical significance is evaluated against statistical independence [1]. For mathematical convenience spike trains are thereby often modeled as Poisson processes. However, experimental data clearly contradicts the Poisson assumption in two ways: (1) Cortical spike trains under stationary conditions are more regular than Poisson spike trains [2], and (2) cortical neurons exhibit a significant negative serial correlation of neighbouring intervals [3]. We briefly review the experimental literature to determine the physiological plausible range for the coefficient of variation (CV) of the inter-spike interval (ISI) distribution and the the serial correlation coefficient β1 of serial order 1. Recently we showed [4] that the coefficient of variation (CV) of the inter-spike interval (ISI) distribution of the individual spike trains indeed has an impact on the significance estimation. Here, we extend this study by investigating how the significance estimation of coincident spikes in pairs of neurons is influenced by the model parameters CV and β1. Based on realizations of a previously established autoregressive point process model [5] we compare coincidence probability distribution of processes with marginal log-normal interval distribution (ARLN) with distributions resulting from Poisson processes. The ARLN model allows to independently vary the parameters of β1 and CV. To this end we numerically construct distributions of coincidence counts from pairs of independent realizations of ARLN processes to realize the null-hypothesis of independence. To gain insight into potential occurrences of false positives if Poisson processes are assumed, we estimate the p-value of spike coincidences resulting from the ARLN model given the significance level α valid for the Poisson process. We find that negative serial correlation within the physiological range decreases the number of significantly evaluated coincidences below the expected level (p-value > α), while positive correlations increase the significant outcomes with respect to the renewal case of serially independent intervals. Also, processes that are more regular than Poisson within the physiological range decrease the number of significant outcomes, while more irregular processes tend to lead to false positives. Our results demonstrate that the p-values are larger than the significance level α for all combinations of β1 and CV that lie within the physiological plausible range. This result shows that the assumption of Poisson statistics implies a conservative strategy where we practically underestimate the true significance of spike coincidences.