On the statistical significance of temporal firing patterns in multi-neuronal spike trains

Repeated occurrences of serial firing sequences of a group of neurons with fixed time delays between neurons are observed in many experiments involving simultaneous recordings from multiple neurons. Such temporal patterns are potentially indicative of underlying microcircuits and it is important to know when a repeatedly occurring pattern is statistically significant. These sequences are typically identified through correlation counts, such as in the two-tape algorithm of Abeles and Gerstein. In this paper we present a method for deciding on the significance of such correlations by characterizing the influence of one neuron on another in terms of conditional probabilities and specifying our null hypothesis in terms of a bound on the conditional probabilities. This method of testing significance of correlation counts is more general than the currently available methods since under our null hypothesis we do not assume that the spiking processes of different neurons are independent. The structure of our null hypothesis also allows us to rank order the detected patterns in terms of the strength of interaction among the neurons constituting the pattern. We demonstrate our method of assessing significance on simulated spike trains involving inhomogeneous Poisson processes with strong interactions, where the correlation counts are obtained using the two-tape algorithm.