Solving the Likelihood Equations for Gaussian Graphical Models

The maximum likelihood degree (ML degree) of a statistical model is the number of complex solutions to the likelihood equations for generic data.  Drton, Sturmfels, and Sullivant have conjectured that the ML degree for Gaussian graphical models when the underlying graph is the $m$-cycle is $(m-3)2^{m-2}+1$. In this talk, we will introduce Gaussian graphical models, explore the ML degree when the underlying graph of the model is a cycle, and present the latest computational results obtained with PHCpack and Bertini.