Message passing on a factor graph is a powerful paradigm for the coding of
approximate inference algorithms for arbitrarily graphical large models. The
notion of a factor graph fragment allows for compartmentalization of algebra
and computer code. We show that the Inverse G-Wishart family of distributions
enables fundamental variational message passing factor graph fragments to be
expressed elegantly and succinctly. Such fragments arise in models for which
approximate inference concerning covariance matrix or variance parameters is
made, and are ubiquitous in contemporary statistics and machine learning
