In genomic applications, there is often interest in identifying genes whose time-course expression trajectories exhibit periodic oscillations with a period of approximately 24 hours. Such genes are usually referred to as circadian, and their identification is a crucial step toward discovering physiological processes that are clock-controlled. It is natural to expect that the expression of gene i at time j might depend to some degree on the expression of the other genes measured at the same time. However, widely-used rhythmicity detection techniques do not accommodate for the potential dependence across genes. We develop a Bayesian approach for periodicity identification that explicitly takes into account the complex dependence structure across time-course trajectories in gene expressions. We employ a latent factor representation to accommodate dependence, while representing the true trajectories in the Fourier domain allows for inference on period, phase, and amplitude of the signal. Identification of circadian genes is allowed through a carefully chosen variable selection prior on the Fourier basis coefficients. The methodology is applied to a novel mouse liver circadian dataset. Although motivated by time-course gene expression array data, the proposed approach is applicable to the analysis of dependent functional data at broad.

翻译：在基因组学应用中，我们常需识别其时间序列表达轨迹呈现约24小时周期振荡的基因。这类基因通常被称为昼夜节律基因，其识别是发现时钟调控生理过程的关键步骤。可以合理预期，基因i在时间j的表达可能在一定程度上依赖于同一时间点上其他被检测基因的表达水平。然而，广泛使用的节律性检测技术并未考虑基因间潜在的相关性。我们提出了一种贝叶斯周期识别方法，该方法明确考虑了基因表达时间轨迹中复杂的依赖结构。我们采用潜在因子表示法处理依赖关系，同时在傅里叶域中表示真实轨迹，从而实现对信号周期、相位和振幅的推断。通过精心选择的傅里叶基系数变量选择先验，我们得以识别昼夜节律基因。该方法已应用于一个新颖的小鼠肝脏昼夜节律数据集。虽然本研究源于时间序列基因表达阵列数据，但所提出的方法广泛适用于依赖型函数数据分析。