- Dimitra Kosta: School of Mathematics and Statistics, University of Glasgow, Glasgow, UK.
- Kaie Kubjas: Department of Mathematics and Systems Analysis, Aalto University, Espoo, Finland. kaie.kubjas@aalto.fi. ORCID
Phylogenetic models admit polynomial parametrization maps in terms of the root distribution and transition probabilities along the edges of the phylogenetic tree. For symmetric continuous-time group-based models, Matsen studied the polynomial inequalities that characterize the joint probabilities in the image of these parametrizations (Matsen in IEEE/ACM Trans Comput Biol Bioinform 6:89-95, 2009). We employ this description for maximum likelihood estimation via numerical algebraic geometry. In particular, we explore an example where the maximum likelihood estimate does not exist, which would be difficult to discover without using algebraic methods.