Multivariate functional data arise in a wide range of applications. One fundamental task is to understand the causal relationships among these functional objects of interest, which has not yet been fully explored. In this article, we develop a novel Bayesian network model for multivariate functional data where the conditional independence and causal structure are both encoded by a directed acyclic graph. Specifically, we allow the functional objects to deviate from Gaussian process, which is adopted by most existing functional data analysis models. The more reasonable non-Gaussian assumption is the key for unique causal structure identification even when the functions are measured with noises. A fully Bayesian framework is designed to infer the functional Bayesian network model with natural uncertainty quantification through posterior summaries. Simulation studies and real data examples are used to demonstrate the practical utility of the proposed model.

翻译：多种应用中产生多种功能数据。一项基本任务是了解这些功能性利益对象之间尚未充分探讨的因果关系。在本条中,我们开发了一个新的贝叶斯网络模型,用于多变量功能数据,有条件的独立和因果结构均由定向环形图编码。具体地说,我们允许功能性对象偏离多数现有功能性数据分析模型采用的高斯进程。更合理的非古西安假设是确定独特因果结构的关键,即使用噪音测量功能。一个完整的巴伊西亚框架旨在推断功能性贝伊斯网络模型,通过外表摘要对自然不确定性进行量化。使用模拟研究和真实数据实例来证明拟议模型的实际用途。