Maximum Likelihood Estimation of Symmetric Group-Based Models via Numerical Algebraic Geometry

Dimitra Kosta, Kaie Kubjas*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)
185 Downloads (Pure)

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.

Original languageEnglish
Pages (from-to)337–360
JournalBulletin of Mathematical Biology
Volume81
Issue number2
DOIs
Publication statusPublished - Feb 2019
MoE publication typeA1 Journal article-refereed

Keywords

  • Algebraic statistics
  • Group-based models
  • Maximum likelihood estimation
  • Numerical algebraic geometry
  • Phylogenetics
  • Real algebraic geometry

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