Closed form jitter methods for neuronal spike train analysis

Interval jitter and spike resampling methods are used to analyze the time scale at which temporal correlations occur in neuronal spike trains. These methods allow the computation of jitter-corrected cross correlograms as well as statistically robust hypothesis testing to decide whether observed correlations at a given time scale are significant. Since currently used Monte Carlo methods are computationally costly, we propose to compute the distribution of the probability of observing a jittered spike train in closed form. We show that this distribution is obtained by computing the analytical solution for each jitter interval and then convolving the distributions of all intervals. For all mean firing rates tested, computing the convolutions in Fourier space rather than directly improves performance considerably without loss of accuracy. Performance increased with mean firing rates and length of spike trains. The method allows for rapid analysis of long spike trains with high accuracy.