  We provide a selected overview of methodology and theory for estimation and
inference on the edge weights in high-dimensional directed and undirected
Gaussian graphical models. For undirected graphical models, two main explicit
constructions are provided: one based on a global method that maximizes the
joint likelihood (the graphical Lasso) and one based on a local (nodewise)
method that sequentially applies the Lasso to estimate the neighbourhood of
each node. The proposed estimators lead to confidence intervals for edge
weights and recovery of the edge structure. We evaluate their empirical
performance in an extensive simulation study. The theoretical guarantees for
the methods are achieved under a sparsity condition relative to the sample size
and regularity conditions. For directed acyclic graphs, we apply similar ideas
to construct confidence intervals for edge weights, when the directed acyclic
graph is identifiable.
