PhD Course: Algebraic statistical models and their maximum likelihood degree

This is a graduate course in algebraic statistics focusing on the maximum likelihood degree (MLD). The MLD is an invariant of algebraic statistical models that measures the algebraic complexity of the maximum likelihood estimation problem on that model. Calculating this number for various families of discrete or continuous models is interesting because it allows exhaustive solutions to this estimation problem. After reviewing the basics and defining the MLD for discrete and Gaussian algebraic models, the course features practical computing sessions to get practice in handling this invariant and computing with it. The last part of the course is theoretical and aimed at understanding recent research on discrete statistical models with maximum likelihood degree one.