Reciprocal ML-degree of Brownian Motion Tree Models

Abstract: Brownian Motion Tree Models (BMTM) are multivariate Gaussian models that arise in phylogenetics when studying the evolution of species through time. They are realized by rooted directed trees. BMTM are wonderful as the space of their covariance matrices is a linear space of symmetric matrices, and the space of their concentration matrices is a toric variety. In applications, one is interested in computing the point in a model that is more probable for the observed data. The (reciprocal) Maximum Likelihood degree of the model gives an insight on the complexity of this problem. In BMTM the reciprocal ML-degree can be nicely computed from the structure of the tree. To prove this result we require help from toric geometry. This is based on joint work with T. Boege, J.I. Coons, C. Eur, and F. Röttger.

combinatorics

Audience: researchers in the topic

York University Applied Algebra Seminar