Title: Some Algebraic Properties of Hierarchical Models

Abstract: We are going to introduce  certain toric ideals that correspond to structures of Hierarchical Models in Algebraic Statistics and explore the properties of these ideals.  One  challenge will be to describe ideals that have infinitely many generators in a finite way, which we do using the symmetry group action on the set of indices. We will also show a formula for calculating the dimension of the variety defined by these ideals, and make progress in calculating the corresponding Hilbert function.