We propose the first Bayesian methods for detecting change points in high-dimensional mean and covariance structures. These methods are constructed using pairwise Bayes factors, leveraging modularization to identify significant changes in individual components efficiently. We establish that the proposed methods consistently detect and estimate change points under much milder conditions than existing approaches in the literature. Additionally, we demonstrate that their localization rates are nearly optimal in terms of rates. The practical performance of the proposed methods is evaluated through extensive simulation studies, where they are compared to state-of-the-art techniques. The results show comparable or superior performance across most scenarios. Notably, the methods effectively detect change points whenever signals of sufficient magnitude are present, irrespective of the number of signals. Finally, we apply the proposed methods to genetic and financial datasets, illustrating their practical utility in real-world applications.

翻译：本文首次提出了检测高维均值与协方差结构变点的贝叶斯方法。这些方法通过成对贝叶斯因子构建，利用模块化设计高效识别各分量的显著变化。我们证明，相较于文献中现有方法，所提方法能在更宽松的条件下一致地检测并估计变点。此外，我们论证了其定位速率在速率意义下近乎最优。通过大量模拟研究，我们将所提方法与前沿技术进行比较，评估了其实际性能。结果显示，在多数场景中该方法具有相当或更优的表现。值得注意的是，只要存在足够强度的信号，无论信号数量多少，该方法均能有效检测变点。最后，我们将所提方法应用于遗传学与金融数据集，展示了其在现实应用中的实用价值。