  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.
