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arXiv · 2107.04516

Staged tree models with toric structure

Christiane Görgen·Aida Maraj·Lisa Nicklasson
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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.

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Christiane Görgen, Aida Maraj, Lisa Nicklasson. 2021-07-23. Staged tree models with toric structure. https://doi.org/10.1016/j.jsc.2022.04.006

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