The estimation of the covariance matrix is a key concern in the analysis of longitudinal data. When data consist of multiple groups, it is often assumed the covariance matrices are either equal across groups or are completely distinct. We seek methodology to allow borrowing of strength across potentially similar groups to improve estimation. To that end, we introduce a covariance partition prior that proposes a partition of the groups at each measurement time. Groups in the same set of the partition share dependence parameters for the distribution of the current measurement given the preceding ones, and the sequence of partitions is modeled as a Markov chain to encourage similar structure at nearby measurement times. This approach additionally encourages a lower-dimensional structure of the covariance matrices by shrinking the parameters of the Cholesky decomposition toward zero. We demonstrate the performance of our model through two simulation studies and the analysis of data from a depression study. This article includes Supplementary Materials available online.

中文翻译：

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协方差划分先验：一种用于纵向数据同时协方差估计的贝叶斯方法

协方差矩阵的估计是纵向数据分析中的一个关键问题。当数据由多个组组成时，通常假设协方差矩阵在组间相等或完全不同。我们寻求方法来允许在可能相似的群体之间借用实力来改进估计。为此，我们引入了先验协方差分区，它在每个测量时间提出了组的分区。同一分区组中的组共享当前测量值分布的相关参数，并且分区序列被建模为马尔可夫链，以在附近的测量时间鼓励相似的结构。这种方法还通过将 Cholesky 分解的参数向零缩小来鼓励协方差矩阵的低维结构。我们通过两项模拟研究和对抑郁症研究数据的分析来证明我们模型的性能。本文包括在线提供的补充材料。