Functional data analysis, which models data as realizations of random functions over a continuum, has emerged as a useful tool for time series data. Often, the goal is to infer the dynamic connections (or time-varying conditional dependencies) among multiple functions or time series. For this task, a dynamic and Bayesian functional graphical model is introduced. The proposed modeling approach prioritizes the careful definition of an appropriate graph to identify both time-invariant and time-varying connectivity patterns. A novel block-structured sparsity prior is paired with a finite basis expansion, which together yield effective shrinkage and graph selection with efficient computations via a Gibbs sampling algorithm. Crucially, the model includes (one or more) graph changepoints, which are learned jointly with all model parameters and incorporate graph dynamics. Simulation studies demonstrate excellent graph selection capabilities, with significant improvements over competing methods. The proposed approach is applied to study of dynamic connectivity patterns of sea surface temperatures in the Pacific Ocean and reveals meaningful edges.

翻译：函数数据分析将数据建模为连续域上随机函数的实现，已成为时间序列分析的有效工具。其目标通常是推断多个函数或时间序列间的动态关联（或时变条件依赖关系）。为此，本文提出一种动态贝叶斯函数图模型。该建模方法强调通过精确定义合适的图结构，以识别时不变与时变的连接模式。模型结合了新颖的块结构稀疏先验与有限基展开，二者共同通过吉布斯采样算法实现有效的收缩效应、图选择与高效计算。关键的是，模型包含（一个或多个）图结构变点，这些变点与所有模型参数联合学习，并融入了图动态特性。仿真研究表明该方法具有优异的图选择能力，较现有方法有显著提升。所提方法应用于太平洋海表温度动态连接模式的研究，揭示了具有物理意义的关联边。