Multiple Tests based on a Gaussian Approximation of the Unitary Events method
Résumé
The Unitary Events (UE) method is one of the most popular and efficient method used this last decade to detect conspicuous patterns of coincident joint spike ac- tivity among simultaneously recorded neurons. The detection of coincidences was first based on a binning procedure (Grün, 1996), which lead to some defects. These defects were then corrected with the Multiple Shifts (MS) procedure (Grün et al, 1999). Starting from this last step, we propose here some new improvements. We mainly show that the delayed coincidences count cannot be Poisson distributed if it is assumed that the spike trains are both Poisson and stationary processes. The gap between the real distribution and the Poisson one increases with the firing rate and the allowed delay for the coincidences. Moreover we precisely compute the asymptotic Gaussian distribution of the difference between the observed coincidences count and an estimate of the expected count, showing that the replacement of the expected count by an estimate changes the law itself. This leads to statistical tests that are proved to be asymptotically of prescribed level α. In practice, the UE method is applied simultaneously over different sliding windows and all the tests with p-values less than 0.05 are declared detected. However it is well known in multiple testing theory that this method does not guarantee any control in terms of False Discovery Rate. We combine our new tests on sliding windows with a Benjamini and Hochberg approach (1995) leading to the Multiple Tests based on a Gaussian Approximation of the Unitary Events (MTGAUE) method. MTGAUE is tested on simulated spike trains and applied on real neuronal data. Finally, MT- GAUE is not only mathematically more rigorous but it also proves to be reliable over a larger range of parameters than the original UE method.
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