Equivalence Classes of Staged Trees
Christiane G\"orgen, Jim Q. Smith

TL;DR
This paper characterizes the statistical equivalence classes of staged trees and CEGs, showing they share a polynomial description and can be transformed through simple polynomial operations, with applications to real data analysis.
Contribution
It provides a complete characterization of equivalence classes of staged trees and CEGs using polynomial descriptions and transformation methods.
Findings
All graphical representations of the same model share a common polynomial description.
Transformations on the polynomial enable traversal of equivalence classes.
Application to real data illustrates the method's practical utility.
Abstract
In this paper we give a complete characterization of the statistical equivalence classes of CEGs and of staged trees. We are able to show that all graphical representations of the same model share a common polynomial description. Then, simple transformations on that polynomial enable us to traverse the corresponding class of graphs. We illustrate our results with a real analysis of the implicit dependence relationships within a previously studied dataset.
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