Functional brain imaging through electroencephalography (EEG) relies upon the analysis and interpretation of high-dimensional, spatially organized time series. We propose to represent time-localized frequency domain characterizations of EEG data as region-referenced functional data. This representation is coupled with a hierarchical regression modeling approach to multivariate functional observations. Within this familiar setting we discuss how several prior models relate to structural assumptions about multivariate covariance operators. An overarching modeling framework, based on infinite factorial decompositions, is finally proposed to balance flexibility and efficiency in estimation. The motivating application stems from a study of implicit auditory learning, in which typically developing (TD) children, and children with autism spectrum disorder (ASD) were exposed to a continuous speech stream. Using the proposed model, we examine differential band power dynamics as brain function is interrogated throughout the duration of a computer-controlled experiment. Our work offers a novel look at previous findings in psychiatry and provides further insights into the understanding of ASD. Our approach to inference is fully Bayesian and implemented in a highly optimized Rcpp package.

中文翻译：

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EEG 信号的区域参考频谱功率动态：一种分层建模方法

通过脑电图 (EEG) 进行的功能性大脑成像依赖于对高维、空间组织的时间序列的分析和解释。我们建议将 EEG 数据的时域化频域特征表示为区域参考功能数据。这种表示与多变量功能观察的分层回归建模方法相结合。在这个熟悉的环境中，我们讨论了几个先验模型如何与关于多元协方差算子的结构假设相关。最后提出了一个基于无限阶乘分解的总体建模框架，以平衡估计的灵活性和效率。激励应用源于对内隐听觉学习的研究，其中典型的发育 (TD) 儿童，和患有自闭症谱系障碍 (ASD) 的儿童接触到连续的语音流。使用所提出的模型，我们在计算机控制实验的整个持续时间内检查大脑功能时的差分频带功率动态。我们的工作提供了对精神病学先前发现的新颖看法，并提供了对 ASD 理解的进一步见解。我们的推理方法是完全贝叶斯的，并在高度优化的 Rcpp 包中实现。