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Multivariate functional data arise in a wide range of applications. Onefundamental task is to understand the causal relationships among thesefunctional objects of interest, which has not yet been fully explored. In thisarticle, we develop a novel Bayesian network model for multivariate functionaldata where the conditional independence and causal structure are both encodedby a directed acyclic graph. Specifically, we allow the functional objects todeviate from Gaussian process, which is adopted by most existing functionaldata analysis models. The more reasonable non-Gaussian assumption is the keyfor unique causal structure identification even when the functions are measuredwith noises. A fully Bayesian framework is designed to infer the functionalBayesian network model with natural uncertainty quantification throughposterior summaries. Simulation studies and real data examples are used todemonstrate the practical utility of the proposed model.

Functional Bayesian Networks for Discovering Causality from Multivariate Functional Data