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Staged trees are a recently-developed, powerful family of probabilisticgraphical models. An equivalence class of staged trees has now beencharacterised, and two fundamental statistical operators have been defined totraverse the equivalence class of a given staged tree. Here, two staged treesare said to be statistically equivalent when they represent the same set ofdistributions. Probabilistic graphical models such as staged trees areincreasingly being used for causal analyses. Staged trees which are within thesame equivalence class can encode very different causal hypotheses but dataalone cannot help us distinguish between these. Therefore, in using score-basedmethods to learn the model structure and distributions from data for causalanalyses, we should expect that a suitable scoring function is one whichassigns the same score to statistically equivalent models. No scoring functionhas yet been proven to have this desirable property for staged trees. In thispaper, we present a novel Bayesian Dirichlet scoring function based on pathuniformity and mass conversation, and prove that this new scoring function isscore-equivalent for staged trees.

Score Equivalence for Staged Trees