Logarithmic Voronoi Cells

Using both Monodromy (Taylor's lecture) and Parameter Homotopies (Sascha's lecture) we will apply Numerical Nonlinear Algebra to statistics. Usually, a Voronoi cell is the subset of points closest to your favorite point, as measured by Euclidean distance. If your favorite point lies on a statistical model, the log-likelihood function (of maximum likelihood estimation) can replace Euclidean distance, and the resulting Voronoi cells are called logarithmic. All points in a logarithmic Voronoi cell have the same maximum likelihood estimate on the statistical model. We will use Numerical Nonlinear Algebra to compute the logarithmic Voronoi cells of our favorite point on a statistical model, and observe directly their (sometimes) nonlinear boundaries.