Detection of dependence patterns with delay

The Unitary Events (UE) method is a popular and efficient method used this last decade to detect dependence patterns of joint spike activity among simultaneously recorded neurons. The first introduced method is based on binned coincidence count \citep{Grun1996} and can be applied on two or more simultaneously recorded neurons. Among the improvements of the methods, a transposition to the continuous framework has recently been proposed in \citep{muino2014frequent} and fully investigated in \citep{MTGAUE} for two neurons. The goal of the present paper is to extend this study to more than two neurons. The main result is the determination of the limit distribution of the coincidence count. This leads to the construction of an independence test between $L\geq 2$ neurons. Finally we propose a multiple test procedure via a Benjamini and Hochberg approach \citep{Benjamini1995}. All the theoretical results are illustrated by a simulation study, and compared to the UE method proposed in \citep{Grun2002}. Furthermore our method is applied on real data

Bootstrap and permutation tests of independence for point processes

Motivated by a neuroscience question about synchrony detection in spike train analysis, we deal with the independence testing problem for point processes. We introduce non-parametric test statistics, which are rescaled general $U$-statistics, whose corresponding critical values are constructed from bootstrap and randomization/permutation approaches, making as few assumptions as possible on the underlying distribution of the point processes. We derive general consistency results for the bootstrap and for the permutation w.r.t. to Wasserstein's metric, which induce weak convergence as well as convergence of second order moments. The obtained bootstrap or permutation independence tests are thus proved to be asymptotically of the prescribed size, and to be consistent against any reasonable alternative. A simulation study is performed to illustrate the derived theoretical results, and to compare the performance of our new tests with existing ones in the neuroscientific literature

tapraid5/a5-cplx/a5-cplx/a50203/a50063-03a heckt S�4 6/18/03 13:08 Art: RA02-478 Input-css(css) Significance of Joint-Spike Events Based on Trial-Shuffling by Efficient Combinatorial Methods

The assembly hypothesis suggests that information processing in the cortex is mediated by groups of neurons expressed by their coordinated spiking activity. Thus, the unitary events analysis was designed to detect the presence of conspicuous joint-spike events in multiple single-unit recordings and to evaluate their statistical significance. The null hypothesis of the associated test assumes independent Poisson processes and leads to parametric significance estimation. In order to allow for arbitrary processes here we suggest to base the significance estimation on trial shuffling and resampling. In this scheme the null hypothesis is implemented by combining spike trains from nonsimultaneous trials and counting the joint-spike events. The coincidence distribution serving for the significance estimation is generated by repetitive resampling. The number of all possible recombinations, however, grows dramatically with the number of trials and neurons and thus is not practical for a user-interactive implementation of the analysis. We have suggested a Monte-Carlo-based resampling procedure and demonstrated that the procedure yields an appropriate estimate of the distribution and reliable significance estimation. In contrast, here, we present an exact solution. Rewriting the statistical problem in terms of certain macrostates, we are able to systematically sample the coincidence counts from all trial combinations. In addition we restrict the generating process to those counts forming the relevant tail of the distribution. The computationally effective implementation uses the concep