Families of Polytopes with Rational Linear Precision in Higher Dimensions

Abstract In this article, we introduce a new family of lattice polytopes with rational linear precision. For purpose, define class discrete statistical models that call multinomial staged tree models. We prove these have maximum likelihood estimators (MLE) and give criterion for to be log-linear. Our main result is then obtained by applying Garcia-Puente Sottile’s theorem establishes correspondence between precision log-linear MLE. Throughout also study the interplay primitive collections normal fan polytope shape Horn matrix its corresponding model. Finally, investigate arising from toric models, in terms combinatorics their representations.