  Gaussian graphical models are used throughout the natural sciences, social
sciences, and economics to model the statistical relationships between
variables of interest in the form of a graph. We here provide a pedagogic
introduction to Gaussian graphical models and review recent results on maximum
likelihood estimation for such models. Throughout, we highlight the rich
algebraic and geometric properties of Gaussian graphical models and explain how
these properties relate to convex optimization and ultimately result in
insights on the existence of the maximum likelihood estimator (MLE) and
algorithms for computing the MLE.
