A staged tree model is a discrete statistical model encoding relationships between events. These models are realised by directed trees with coloured vertices. In algebro-geometric terms, the model consists of points inside a toric variety. For certain trees, called balanced, the model is in fact the intersection of the toric variety and the probability simplex. We will see that its defining toric ideal is Kosul, normal, and it has a generating set with binomials of degree one and two. Most importantly, the class of staged tree models with a toric structure extends far outside of the balanced case, if we allow a change of coordinates. The talk is based on the preprint, "Staged tree models with toric structure" (arXiv:2107.04516) with Christiane Gorgen and Lisa Nicklasson.
Speaker(s): Aida Maraj (UM)