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, we propose a dynamic and Bayesian functional graphical model. Our modeling approach prioritizes the careful definition of an appropriate graph to identify both time-invariant and time-varying connectivity patterns. We introduce a novel block-structured sparsity prior 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. We apply the proposed approach to study of dynamic connectivity patterns of sea surface temperatures in the Pacific Ocean and discovers meaningful edges.

翻译：函数型数据分析将数据建模为连续域上随机函数的实现，已成为时间序列数据分析的有力工具。通常，研究目标是推断多个函数或时间序列之间的动态连接（即随时间变化的条件依赖关系）。针对此问题，我们提出了一种动态贝叶斯函数图模型。该建模方法着重于精确定义合适的图结构，以识别时不变与时变连接模式。我们引入了一种新颖的块结构稀疏性先验，并结合有限基展开，通过吉布斯采样算法实现有效的收缩与图选择，同时保证计算高效性。关键在于，该模型包含（一个或多个）图变点，这些变点与所有模型参数联合学习，并整合了图动态特性。仿真研究表明，该方法具有卓越的图选择能力，显著优于对比方法。我们将所提方法应用于太平洋海表温度的动态连接模式研究，并发现了有意义的边结构。