This paper is motivated by a cutting-edge application in neuroscience: the analysis of electroencephalogram (EEG) signals recorded under flash stimulation. Under commonly used signal-processing assumptions, only the phase angle of the EEG is required for the analysis of such applications. We demonstrate that these assumptions imply that the phase has a projected isotropic normal distribution. We revisit this distribution and derive several new properties, including closed-form expressions for its trigonometric moments. We then examine the distribution of the mean resultant and its square -- a statistic of central importance in phase-based EEG studies. The distribution of the resultant is analytically intricate; to make it practically useful, we develop two approximations based on the well-known resultant distribution for the von Mises distribution. We then study inference problems for this projected isotropic normal distribution. The method is illustrated with an application to EEG data from flash-stimulation experiments.

翻译：本文的动机源于神经科学中的一项前沿应用：闪光刺激下记录的脑电图（EEG）信号分析。在常用的信号处理假设下，此类应用的分析仅需EEG信号的相位角。我们证明，这些假设意味着相位服从投影各向同性正态分布。我们重新审视该分布，并推导了若干新性质，包括其三角矩的闭式表达式。随后，我们研究了平均合向量及其平方的分布——这是基于相位的EEG研究中至关重要的统计量。合向量的分布解析上较为复杂；为使其具有实际应用价值，我们基于von Mises分布中已知的合向量分布，提出了两种近似方法。接着，我们研究了该投影各向同性正态分布的推断问题。最后，通过闪光刺激实验的EEG数据应用示例对该方法进行了说明。