Open Access
May 2008 Symmetric measures via moments
Alexey Koloydenko
Bernoulli 14(2): 362-390 (May 2008). DOI: 10.3150/07-BEJ6144


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.


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Alexey Koloydenko. "Symmetric measures via moments." Bernoulli 14 (2) 362 - 390, May 2008.


Published: May 2008
First available in Project Euclid: 22 April 2008

zbMATH: 1155.62001
MathSciNet: MR2544092
Digital Object Identifier: 10.3150/07-BEJ6144

Keywords: Algebraic statistics , determinate measures , finite groups , linear transformations , log-linear models , maximum entropy , Polynomial invariants , symmetry , toric models

Rights: Copyright © 2008 Bernoulli Society for Mathematical Statistics and Probability

Vol.14 • No. 2 • May 2008
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