Symmetric measures via moments

Details Symmetric measures via moments Symmetric measures via moments

2004-06-09

arxiv.org/abs/math/0406173v2

Bernoulli 2008, Vol. 14, No. 2, 362-390

Mathematics

Probability

Published in at http://dx.doi.org/10.3150/07-BEJ6144 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statist

Scientific paper

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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