Functional Bayesian networks for discovering causality from multivariate functional data.

Area of Science:

• Statistics
• Machine Learning
• Causal Inference

Background:

• Multivariate functional data are prevalent across diverse scientific fields.
• Understanding causal relationships among these data is a fundamental challenge.
• Existing methods may struggle with unique causal structure identification, especially with noisy functional data.

Purpose of the Study:

• To develop a novel Bayesian network (BN) model for multivariate functional data.
• To enable the identification of conditional independencies and causal structures using directed acyclic graphs.
• To address limitations in causal structure identification for non-Gaussian functional processes.

Main Methods:

• Developed a Bayesian network (BN) model tailored for multivariate functional data.
• Incorporated directed acyclic graphs to encode conditional independencies and causal structure.
• Utilized a fully Bayesian framework for model inference and uncertainty quantification.

Main Results:

• The proposed model allows functional objects to deviate from Gaussian processes, crucial for unique causal structure identification.
• The Bayesian framework provides natural uncertainty quantification through posterior summaries.
• Simulation studies and real-world examples validate the model's practical utility.

Conclusions:

• The novel Bayesian network model effectively captures causal relationships in multivariate functional data.
• The approach offers robust causal structure identification, even in the presence of noise.
• The method provides a valuable tool for analyzing complex functional data across various applications.