In this paper, we give a complete characterization of the statistical equivalence classes of CEGs and of staged trees. We are able to show that all graphical representations of the same model share a common polynomial description. Then, simple transformations on that polynomial enable us to traverse the corresponding class of graphs. We illustrate our results with a real analysis of the implicit dependence relationships within a previously studied dataset.
"Equivalence classes of staged trees." Bernoulli 24 (4A) 2676 - 2692, November 2018. https://doi.org/10.3150/17-BEJ940