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 known to be exactly the intersection of the toric variety and the probability simplex. We show that in this case the defining toric ideal is Kosul, normal, and it has a Gröbner basis with binomials of degree one and two. The highlight of the talk will be that the class of staged tree models with a toric structure extends far outside of balanced trees, if we allow a change of coordinates. The talk is based on the preprint (https://arxiv.org/abs/2107.04516) with Christiane Görgen and Lisa Nicklasson.
Staged Tree Models with Toric Structure
Aida Maraj, University of MichiganAuthors: Christiane Görgen, Aida Maraj, Lisa Nicklasson
2022 AWM Research Symposium
Homological and Combinatorial Aspects of Commutative Algebra