Maximum likelihood estimation of symmetric group-based models via numerical algebraic geometry

Kosta, D. and Kubjas, K. (2019) Maximum likelihood estimation of symmetric group-based models via numerical algebraic geometry. Bulletin of Mathematical Biology, 81(2), pp. 337-360. (doi: 10.1007/s11538-018-0523-2) (PMID:30357599) (PMCID:PMC6342846)

Abstract

Phylogenetic models admit polynomial parametrization maps in terms of the root distribution and transition probabilities along the edges of the phylogenetic tree. For symmetric continuous-time group-based models, Matsen studied the polynomial inequalities that characterize the joint probabilities in the image of these parametrizations (Matsen in IEEE/ACM Trans Comput Biol Bioinform 6:89–95, 2009). We employ this description for maximum likelihood estimation via numerical algebraic geometry. In particular, we explore an example where the maximum likelihood estimate does not exist, which would be difficult to discover without using algebraic methods.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Kosta, Dr Dimitra
• Authors: Kosta, D., and Kubjas, K.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Bulletin of Mathematical Biology
• Publisher: Springer
• ISSN: 0092-8240
• ISSN (Online): 1522-9602
• Published Online: 24 October 2018
• Copyright Holders: Copyright © 2018 The Authors
• First Published: First published in Bulletin of Mathematical Biology 81(2): 337-360
• Publisher Policy: Reproduced under a Creative Commons License