Groebner Bases of Reducible Hierarchical Models

In this talk, I will introduce general hierarchical models from statistics. From the algebraic perspective, these are toric ideals parametrized by a simplicial complex and a nonnegative integer vector. I will show how to build up Groebner bases for these toric ideals when the underlying simplicial complex is reducible and discuss the statistical applications of these algebraic results. Joint work with Serkan Hosten.