  We study the problem of automatically discovering Granger causal relations
from observational multivariate time-series data.Vector autoregressive (VAR)
models have been time-tested for this problem, including Bayesian variants and
more recent developments using deep neural networks. Most existing VAR methods
for Granger causality use sparsity-inducing penalties/priors or post-hoc
thresholds to interpret their coefficients as Granger causal graphs. Instead,
we propose a new Bayesian VAR model with a hierarchical factorised prior
distribution over binary Granger causal graphs, separately from the VAR
coefficients. We develop an efficient algorithm to infer the posterior over
binary Granger causal graphs. Comprehensive experiments on synthetic,
semi-synthetic, and climate data show that our method is more uncertainty
aware, has less hyperparameters, and achieves better performance than competing
approaches, especially in low-data regimes where there are less observations.
