On the ideals of equivariant tree models

Details On the ideals of equivariant tree models On the ideals of equivariant tree models

2007-12-19

arxiv.org/abs/0712.3230v3

Mathematics

Algebraic Geometry

23 pages. Greatly improved exposition, in part following suggestions by a referee--thanks! Also added example

Scientific paper

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.

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