Perturbation method for determining the group of invariance of hierarchical models
Abstract
We propose a perturbation method for determining the (largest) group of invariance of a toric ideal defined in Aoki and Takemura [2008a]. In the perturbation method, we investigate how a generic element in the row space of the configuration defining a toric ideal is mapped by a permutation of the indeterminates. Compared to the proof in Aoki and Takemura [2008a] which was based on stabilizers of a subset of indeterminates, the perturbation method gives a much simpler proof of the group of invariance. In particular, we determine the group of invariance for a general hierarchical model of contingency tables in statistics, under the assumption that the numbers of the levels of the factors are generic. We prove that it is a wreath product indexed by a poset related to the intersection poset of the maximal interaction effects of the model.
Keywords
Cite
@article{arxiv.0808.2725,
title = {Perturbation method for determining the group of invariance of hierarchical models},
author = {Tomonari Sei and Satoshi Aoki and Akimichi Takemura},
journal= {arXiv preprint arXiv:0808.2725},
year = {2009}
}
Comments
17pages, no figures