Symmetric measures via moments. (English) Zbl 1155.62001

Summary: Algebraic tools in statistics have recently been receiving special attention and a number of interactions between algebraic geometry and computational statistics have been rapidly developing. This paper presents another such connection, namely, one between probabilistic models invariant under a finite group of (non-singular) linear transformations and polynomials invariant under the same group. Two specific aspects of the connection are discussed: generalization of the (uniqueness part of the multivariate) problem of moments and log-linear, or toric, modeling by expansion of invariant terms. A distribution of minuscule subimages extracted from a large database of natural images is analyzed to illustrate the above concepts.


62A01 Foundations and philosophical topics in statistics
20G99 Linear algebraic groups and related topics
62H35 Image analysis in multivariate analysis


Magma; Macaulay2; INVAR; GAP
Full Text: DOI arXiv


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