Brownian motion tree models are toric

Bernd Sturmfels; Caroline Uhler; Piotr Zwiernik

Kybernetika (2020)

  • Volume: 56, Issue: 6, page 1154-1175
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Sturmfels, Bernd, Uhler, Caroline, and Zwiernik, Piotr. "Brownian motion tree models are toric." Kybernetika 56.6 (2020): 1154-1175. <http://eudml.org/doc/297092>.

@article{Sturmfels2020,
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.},
author = {Sturmfels, Bernd, Uhler, Caroline, Zwiernik, Piotr},
journal = {Kybernetika},
keywords = {Brownian motion tree model; ultrametric matrices; toric geometry},
language = {eng},
number = {6},
pages = {1154-1175},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Brownian motion tree models are toric},
url = {http://eudml.org/doc/297092},
volume = {56},
year = {2020},
}

TY - JOUR
AU - Sturmfels, Bernd
AU - Uhler, Caroline
AU - Zwiernik, Piotr
TI - Brownian motion tree models are toric
JO - Kybernetika
PY - 2020
PB - Institute of Information Theory and Automation AS CR
VL - 56
IS - 6
SP - 1154
EP - 1175
AB - 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.
LA - eng
KW - Brownian motion tree model; ultrametric matrices; toric geometry
UR - http://eudml.org/doc/297092
ER -

References

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