We develop and study a statistical test to detect synchrony in spike trains. Our test is based on the number of coincidences between two trains of spikes. The data are supplied in the form of \(n\) pairs (assumed to be independent) of spike trains. The aim is to assess whether the two trains in a pair are also independent. Our approach is based on previous results of Albert et al. (2015, 2019) and Kim et al. (2022) that we extend to our setting, focusing on the construction of a non-asymptotic criterion ensuring the detection of synchronization in the framework of permutation tests. Our criterion is constructed such that it ensures the control of the Type II error, while the Type I error is controlled by construction. We illustrate our results within two classical models of interacting neurons, the jittering Poisson model and Hawkes processes having \(M\) components interacting in a mean field frame and evolving in stationary regime. For this latter model, we obtain a lower bound of the size \(n\) of the sample necessary to detect the dependency between two neurons.

翻译：我们开发并研究了一种统计检验方法，用于检测尖峰序列中的同步性。该检验基于两个尖峰序列之间的重合次数。数据以n对（假设相互独立）尖峰序列的形式提供，旨在评估一对序列中的两个序列是否独立。我们的方法基于Albert等人（2015、2019）及Kim等人（2022）的先前结果，并将其扩展至本文场景，重点构建一个非渐近判据，以确保在置换检验框架下能检测同步性。所构建的判据能够确保对第二类错误的控制，而第一类错误则通过构造方式自动控制。我们通过两种经典的神经元交互模型——抖动泊松模型和具有M个分量、在平均场框架下相互作用且处于稳态演化的霍克斯过程——展示了结果。对于后一种模型，我们得出了检测两个神经元之间依赖关系所需样本量n的下界。