Equations defining probability tree models. (July 2020)

• Record Type: Journal Article
• Authors: Duarte, Eliana; Görgen, Christiane
• Is Part Of: Journal of symbolic computation. Volume 99(2020)
• Page Start: 127
• Page End: 146
• Publication Date: 2020-07
• Subjects: Algebraic geometry -- Algebraic statistics -- Graphical models -- Staged trees; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2019.04.001
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: 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.