  Graph Neural Networks (GNN) provide a powerful framework that elegantly
integrates Graph theory with Machine learning for modeling and analysis of
networked data. We consider the problem of quantifying the uncertainty in
predictions of GNN stemming from modeling errors and measurement uncertainty.
We consider aleatoric uncertainty in the form of probabilistic links and noise
in feature vector of nodes, while epistemic uncertainty is incorporated via a
probability distribution over the model parameters. We propose a unified
approach to treat both sources of uncertainty in a Bayesian framework, where
Assumed Density Filtering is used to quantify aleatoric uncertainty and Monte
Carlo dropout captures uncertainty in model parameters. Finally, the two
sources of uncertainty are aggregated to estimate the total uncertainty in
predictions of a GNN. Results in the real-world datasets demonstrate that the
Bayesian model performs at par with a frequentist model and provides additional
information about predictions uncertainty that are sensitive to uncertainties
in the data and model.
