Symmetric phylogenetic group-based models using numerical algebraic geometry.
Dimitra Kosta (University of Glasgow)
Thursday 16th November, 2017 14:00-15:00 311B Mathematics and Statistics Building
(Lunch with the speaker will be at One A The Square, leaving from the school front foyer at 12.45.)
Phylogenetic models have polynomial parametrization maps. For symmetric group-based models, Matsen studied the polynomial inequalities that characterize the joint probabilities in the image of these parametrizations. 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. We also study the embedding problem for symmetric group-based models, i.e. we identify which mutation matrices are matrix exponentials of rate matrices that are invariant under a group action.