Title: On Toric Ideals of some Statistical Models.

Abstract: We introduce hierarchical models from statistics and their associated Markov bases. These bases are often large and difficult to compute. We introduce certain toric ideals and their algebraic properties as an alternative way of thinking about these objects. One challenge is to describe hierarchical models with infinitely many generators in a finite way. Using a symmetric group action, we describe certain classes of models including progress made for the non-reducible Models. This is joint work with Uwe Nagel.