  In this paper we extend earlier work on groups acting on Gaussian graphical
models to Gaussian Bayesian networks and more general Gaussian models defined
by chain graphs. We discuss the maximal group which leaves a given model
invariant and provide basic statistical applications of this result. This
includes equivariant estimation, maximal invariants and robustness. The
computation of the group requires finding the essential graph. However, by
applying Studeny's theory of imsets we show that computations for DAGs can be
performed efficiently without building the essential graph. In our proof we
derive simple necessary and sufficient conditions on vanishing sub-minors of
the concentration matrix in the model.
