  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.
