MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Equations defining probability tree models

Christiane Görgen and Eliana Maria Duarte Gelvez


Coloured probability tree models are statistical models coding conditional independence between events depicted in a tree graph. They are more general than the very important class of context- specific Bayesian networks. In this paper, we study the algebraic properties of their ideal of model invariants. The generators of this ideal can be easily read from the tree graph and have a straightforward interpretation in terms of the underlying model: they are differences of odds ratios coming from conditional probabilities. One of the key findings in this analysis is that the tree is a convenient tool for understanding the exact algebraic way in which the sum-to-1 conditions on the parameter space translate into the sum-to-one conditions on the joint probabilities of the statistical model. This enables us to identify necessary and sufficient graphical conditions for a staged tree model to be a toric variety intersected with a probability simplex.

MSC Codes:
62-0, 13P25
algebraic statistics, graphical models, Staged TRees

Related publications

2020 Repository Open Access
Christiane Görgen and Eliana Duarte

Equations defining probability tree models

In: Journal of symbolic computation, 99 (2020), pp. 127-146