Department of Statistics, Texas A&M University, College Station, Texas, USA.
Center for Applied Statistics, Institute of Statistics and Big Data, Renmin University of China, Beijing, China.
Biometrics. 2023 Dec;79(4):3279-3293. doi: 10.1111/biom.13922. Epub 2023 Aug 28.
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. In this paper, we develop a novel Bayesian network (BN) model for multivariate functional data where conditional independencies and causal structure are encoded by a directed acyclic graph. Specifically, we allow the functional objects to deviate from Gaussian processes, which is the key to unique causal structure identification even when the functions are measured with noises. A fully Bayesian framework is designed to infer the functional BN model with natural uncertainty quantification through posterior summaries. Simulation studies and real data examples demonstrate the practical utility of the proposed model.
多元函数数据在很多应用中都有出现。其中一个基本任务是理解这些感兴趣的函数对象之间的因果关系。在本文中，我们为多元函数数据开发了一种新的贝叶斯网络（BN）模型，其中条件独立性和因果结构由有向无环图编码。具体来说，我们允许函数对象偏离高斯过程，这是即使在函数受到噪声干扰的情况下也能唯一确定因果结构的关键。我们设计了一个完全贝叶斯框架，通过后验摘要来对函数 BN 模型进行推断，并进行自然不确定性量化。模拟研究和真实数据示例证明了所提出模型的实际效用。
