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TitleFiniteness for the k-factor model and chirality varieties
Author(s) Jan Draisma
TypeArticle in Journal
AbstractThis paper deals with two families of algebraic varieties arising from applications. First, the k-factor model in statistics, consisting of n × n covariance matrices of n observed Gaussian random variables that are pairwise independent given k hidden Gaussian variables. Second, chirality varieties inspired by applications in chemistry. A point in such a chirality variety records chirality measurements of all k-subsets among an n-set of ligands. Both classes of varieties are given by a parameterisation, while for applications having polynomial equations would be desirable. For instance, such equations could be used to test whether a given point lies in the variety. We prove that in a precise sense, which is different for the two classes of varieties, these equations are finitely characterisable when k is fixed and n grows.
KeywordsFactor analysis, Algebraic statistics, G-Noetherianity
URL http://www.sciencedirect.com/science/article/pii/S0001870809002539
JournalAdvances in Mathematics
Pages243 - 256
Translation No
Refereed No