Staged tree models are a discrete generalization of Bayesian networks. We show that these form curved exponential families and derive their natural parameters, sufficient statistic, and cumulant-generating function as functions of their graphical representation. We give necessary and sufficient graphical criteria for classifying regular subfamilies and discuss implications for model selection.
Christiane Görgen and Manuele Leonelli were supported by the programme “Oberwolfach Leibniz Fellows” of the Mathematisches Forschungsinstitut Oberwolfach in 2017. Orlando Marigliano was supported by International Max Planck Research School and Brummer & Partners MathDataLab.
We are grateful to Giovanni Pistone and to Piotr Zwiernik for discussions during the early stages of this project and to Eva Riccomagno for comments on an earlier version of this paper. We also thank the two anonymous referees for their comments which led to a significant improvent of our results.
Christiane Görgen. Manuele Leonelli. Orlando Marigliano. "The curved exponential family of a staged tree." Electron. J. Statist. 16 (1) 2607 - 2620, 2022. https://doi.org/10.1214/22-EJS1984