Bernoulli

  • Bernoulli
  • Volume 14, Number 2 (2008), 362-390.

Symmetric measures via moments

Alexey Koloydenko

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Abstract

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.

Article information

Source
Bernoulli Volume 14, Number 2 (2008), 362-390.

Dates
First available in Project Euclid: 22 April 2008

Permanent link to this document
https://projecteuclid.org/euclid.bj/1208872109

Digital Object Identifier
doi:10.3150/07-BEJ6144

Mathematical Reviews number (MathSciNet)
MR2544092

Zentralblatt MATH identifier
1155.62001

Keywords
algebraic statistics determinate measures finite groups linear transformations log-linear models maximum entropy polynomial invariants symmetry toric models

Citation

Koloydenko, Alexey. Symmetric measures via moments. Bernoulli 14 (2008), no. 2, 362--390. doi:10.3150/07-BEJ6144. https://projecteuclid.org/euclid.bj/1208872109.


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