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Interval jitter and spike resampling methods are used to analyze the timescale on which temporal correlations occur. They allow the computation ofjitter corrected cross correlograms and the performance of an associatedstatistically robust hypothesis test to decide whether observed correlations ata given time scale are significant. Currently used Monte Carlo methodsapproximate the probability distribution of coincidences. They requiregenerating $N_{\rm MC}$ simulated spike trains of length $T$ and calculatingtheir correlation with another spike train up to lag $\tau_{\max}$. This iscomputationally costly $O(N_{\rm MC} \times T \times \tau_{\max})$ and itintroduces errors in estimating the $p$ value. Instead, we propose to computethe distribution in closed form, with a complexity of $O(C_{\max}\log(C_{\max}) \tau_{\max})$, where $C_{\max}$ is the maximum possible numberof coincidences. All results are then exact rather than approximate, and as aconsequence, the $p$-values obtained are the theoretically best possible forthe available data and test statistic. In addition, simulations with realisticparameters predict a speed increase over Monte Carlo methods of two orders ofmagnitude for hypothesis testing, and four orders of magnitude for computingthe full jitter-corrected cross correlogram.

Closed Form Jitter Analysis of Neuronal Spike Trains