# Orlando Marigliano: Discrete Statistical Models with Rational Maximum Likelihood Estimator

**Time: **
Wed 2019-11-06 13.15

**Location: **
KTH 3418

**Lecturer: **
Orlando Marigliano, Max Planck Institute for Mathematics in the Sciences (Leipzig)

### Abstract

A discrete statistical model is a subset of a probability simplex. Its maximum likelihood estimator is a retraction from that simplex onto the model. For which models is this retraction a rational function? First of all, they are all (semi-)algebraic sets, so we are in the domain of real algebraic geometry. Building on results by Huh and Kapranov on Horn uniformization, I give a characterization of such models and demonstrate it on examples. Joint work with Eliana Duarte and Bernd Sturmfels.