Brownian motion tree models are toric
Statistics Theory
2019-02-27 v1 Algebraic Geometry
Populations and Evolution
Statistics Theory
Abstract
Felsenstein's classical model for Gaussian distributions on a phylogenetic tree is shown to be a toric variety in the space of concentration matrices. We present an exact semialgebraic characterization of this model, and we demonstrate how the toric structure leads to exact methods for maximum likelihood estimation. Our results also give new insights into the geometry of ultrametric matrices.
Keywords
Cite
@article{arxiv.1902.09905,
title = {Brownian motion tree models are toric},
author = {Bernd Sturmfels and Caroline Uhler and Piotr Zwiernik},
journal= {arXiv preprint arXiv:1902.09905},
year = {2019}
}
Comments
22 pages, 4 figures