Corpus ID: 67856397

Brownian motion tree models are toric

@article{Sturmfels2019BrownianMT,
  title={Brownian motion tree models are toric},
  author={Bernd Sturmfels and Caroline Uhler and Piotr Zwiernik},
  journal={arXiv: Statistics Theory},
  year={2019}
}
  • Bernd Sturmfels, Caroline Uhler, Piotr Zwiernik
  • Published 2019
  • Mathematics, Biology
  • arXiv: Statistics Theory
  • 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. 

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