Maximum Likelihood Estimation of Symmetric Group-Based Models via Numerical Algebraic Geometry
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Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Author
Date
2019-02-15
Major/Subject
Mcode
Degree programme
Language
en
Pages
337–360
Series
Bulletin of Mathematical Biology, Volume 81, issue 2
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.Description
Keywords
Algebraic statistics, Group-based models, Maximum likelihood estimation, Numerical algebraic geometry, Phylogenetics, Real algebraic geometry
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Citation
Kosta , D & Kubjas , K 2019 , ' Maximum Likelihood Estimation of Symmetric Group-Based Models via Numerical Algebraic Geometry ' , Bulletin of Mathematical Biology , vol. 81 , no. 2 , pp. 337–360 . https://doi.org/10.1007/s11538-018-0523-2
