Staged tree models with toric structure. (November 2022)

• Record Type: Journal Article
• Authors: Görgen, Christiane; Maraj, Aida; Nicklasson, Lisa
• Is Part Of: Journal of symbolic computation. Volume 113(2022)
• Page Start: 242
• Page End: 268
• Publication Date: 2022-11
• Subjects: Algebraic statistics -- Discrete statistical models -- Staged trees -- Toric ideals -- Toric varieties -- Veronese embedding; 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.2022.04.006
• Languages: English
• ISSNs: 0747-7171

Abstract

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.