Staged tree models with toric structure
Abstract
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. This gives the model a straightforward description, and has computational advantages. In this paper we show that the class of staged tree models with a toric structure extends far outside of the balanced case, if we allow a change of coordinates. It is an open problem whether all staged tree models have toric structure.
- Publication:
-
arXiv e-prints
- Pub Date:
- July 2021
- DOI:
- 10.48550/arXiv.2107.04516
- arXiv:
- arXiv:2107.04516
- Bibcode:
- 2021arXiv210704516G
- Keywords:
-
- Mathematics - Commutative Algebra;
- Mathematics - Statistics Theory;
- 62R01;
- 62A09;
- 13F65;
- 14M25
- E-Print:
- Journal of Symbolic Computation, Volume 113, 2022, Pages 242-268