2021
DOI: 10.1016/j.aam.2020.102119
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Toric geometry of the Cavender-Farris-Neyman model with a molecular clock

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Cited by 11 publications
(17 citation statements)
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“…A sufficient statistic of toric models is often achieved effortlessly from the monomial parametrization of the model in statistics; see for instance hierarchical models [68,121,163], graphical models [97], and balanced staged tree models [77]. In other cases, a linear change of coordinates is needed to reveal the toric structure; see for instance conditional independence models and models arising from Bayesian networks [95], and some group based phylogenetics models [226,58]. The vanishing ideal for the staged tree model Figure 1 is toric in the new variables q 0 = p 0 , q 1 = p 0 + p 1 and q 2 = p 0 + p 1 + p 2 ; see [99].…”
Section: Algebraic Statistics By Aida Marajmentioning
confidence: 99%
“…A sufficient statistic of toric models is often achieved effortlessly from the monomial parametrization of the model in statistics; see for instance hierarchical models [68,121,163], graphical models [97], and balanced staged tree models [77]. In other cases, a linear change of coordinates is needed to reveal the toric structure; see for instance conditional independence models and models arising from Bayesian networks [95], and some group based phylogenetics models [226,58]. The vanishing ideal for the staged tree model Figure 1 is toric in the new variables q 0 = p 0 , q 1 = p 0 + p 1 and q 2 = p 0 + p 1 + p 2 ; see [99].…”
Section: Algebraic Statistics By Aida Marajmentioning
confidence: 99%
“…A sufficient statistics of toric models is often achieved effortlessly from the monomial parametrization of the model in statistics; see for instance hierarchical models [66,115,156], graphical models [93], and balanced staged tree models [75]. In other cases, a linear change of coordinates is needed to reveal the toric structure; see for instance conditional independence models and models arising from Bayesian networks [91], and some group based phylogenetics models [56,215]. The existence of matrix A leads to involvement of polyhedral geometry [24,54].…”
Section: Algebraic Statistics By Aida Marajmentioning
confidence: 99%
“…Polynomials in the vanishing ideal I T " IpV T q are called phylogenetic invariants and a major problem for any phylogenetic model is to describe this ideal. Characterizing the invariants of phylogenetic models began with [10,29] and has been continued by many including but not limited to [3,12,13,31,38].…”
Section: Preliminariesmentioning
confidence: 99%
“…Recently, there has been work on the algebraic structure of network models motivated by the advances that algebraic methods achieved for tree models which include many identifiability results [1,2,5,30,33] and descriptions of the phylogenetic invariants of many tree-based models [3,12,13,31,38]. Algebraic methods have also led to competitive methods for reconstructing trees such as those described in [11,14,16] which all utilize invariants.…”
Section: Introductionmentioning
confidence: 99%