Equations defining probability tree models

• Type: Article in International Scientific Journal
• Date: 2020

Authors

Duarte E. (Author) Other; Görgen C. (Author) Other

Journal

Title: Journal of Symbolic Computation

Vol. 99

Pages: 127-146

ISSN: 0747-7171

Publisher: Elsevier

Indexing

Scopus - 4 Citations

Other information

Authenticus ID: P-00X-9EK

DOI: 10.1016/j.jsc.2019.04.001

Abstract (EN): Staged trees or coloured probability tree models are statistical models coding conditional independence between events depicted in a tree graph. They include the very important class of Bayesian networks as a special case and provide a straightforward graphical tool for handling additional context-specific relationships. In this paper, we study the algebraic properties of their ideal of model invariants. We hereby find that the tree also provides a straightforward combinatorial tool to generalise the existing geometric characterisation of decomposable graphical models and Bayesian networks. In particular, from a staged tree we can directly understand the interplay between local and global sum-to-one conditions, read the generators of that ideal, and determine conditions under which the model is a toric variety intersected with the probability simplex.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 19