Lisa Nicklasson: Toric and non-toric ideals of Bayesian networks

Abstract.

A Bayesian network is a discrete statistical model which can be presented graphically by a directed acyclic graph (DAG). Algebraically such a model can be described as a variety of a homogeneous prime ideal. A statistical model is toric if it is given by a toric variety, or equivalently if the ideal is binomial. In this talk we will discuss which DAG's give rise to toric models, and which do not. In the toric case we also investigate when the binomials are quadratic.