## Bernoulli

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

### Symmetric measures via moments

**Full-text: Open access**

#### 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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