Brownian motion tree models are toric
Name
1902.09905.pdf
Description
Submitted version
Size
740.24 KB
Format
Adobe PDF
Checksum (MD5)
41f128a3cb00adfef3a10e8a02265949
Author(s)
Sturmfels, Bernd
Uhler, Caroline
Zwiernik, Piotr
Date Issued
2021
Journal
Kybernetika
Publisher
Institute of Information Theory and Automation
Citation
Sturmfels, Bernd, Uhler, Caroline and Zwiernik, Piotr. 2021. "Brownian motion tree models are toric." Kybernetika, 56 (6).
Version
Original manuscript
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 char-acterization 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.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Institute for Data, Systems, and Society
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.14736/KYB-2020-6-1154
