We introduce equivariant tree models in algebraic statistics, which unify and generalise existing tree models such as the general Markov model, the strand symmetric model, and group based models. We focus on the ideals of such models. We show how the ideals for general trees can be determined from the ideals for stars. The main novelty is our proof that this procedure yields the entire ideal, not just an ideal defining the model set-theoretically. A corollary of theoretical importance is that the ideal for a general tree is generated by the ideals of its flattenings at vertices.
Additional Metadata
Keywords algebraic statistics, invariant theory, phylogenetics
MSC Special varieties (msc 14Mxx), Applications to biology and medical sciences (msc 62P10)
THEME Logistics (theme 3)
Publisher Springer
Journal Mathematische Annalen
Note Link is to arxiv preprint.
Draisma, J, & Kuttler, J. (2009). On the ideals of equivariant tree models. Mathematische Annalen, 344(0712.3230), 619–644.