Jacob Kuhlin: Classifying Maximum Likelihood Degree for Small Colored Gaussian Graphical Model

Abstract

The Maximum Likelihood Degree (ML degree) of a statistical model is the number of complex critical points of the likelihood function. In this thesis we study this on Colored Gaussian Graphical Models, classifying the ML degree of colored graphs of order up to three. We do this by calculating the rational function degree of the gradient of the log- likelihood. Moreover we find that coloring a graph can lower the ML degree. Finally we calculate solutions to the homaloidal partial differential equation developed by Améndola et al. The code developed for these calculations can be used on graphs of higher orders.