Perturbation method for determining the group of invariance of hierarchical models
Perturbation method for determining the group of invariance of hierarchical models
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DOI：
10.1016/j.aam.2009.02.005
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发表时间：
2008-08
期刊：
影响因子：
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通讯作者：
T. Sei;S. Aoki;A. Takemura
中科院分区：
文献类型：
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作者：
T. Sei;S. Aoki;A. Takemura
我们提出了一种确定环面理想的(最大)不变群的摄动方法，定义在[S.Aoki，A.Takemura，马氏基和环面理想的最大不变群，J.符号计算]中。43(5)(2008)342-358]。在微扰方法中，我们研究了定义环面理想的组态的行空间中的一般元素是如何通过不定项的置换来映射的。与Aoki和Takemura基于不定子集稳定器的证明相比，摄动法给出的不变群证明要简单得多。特别地，在假设因素的水平数是一般的情况下，我们确定了统计中列联表的一般层次模型的不变群。我们证明了它是由一个与模型的最大相互作用的交偏序集相关的偏序集索引的圈积。
We propose a perturbation method for determining the (largest) group of invariance of a toric ideal defined in [S. Aoki, A. Takemura, The largest group of invariance for Markov bases and toric ideals, J. Symbolic Comput. 43 (5) (2008) 342–358]. 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 by Aoki and Takemura 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.