Algebraic Statistics is an emerging discipline that combines generality and long tradition of algebra with statistical techniques, increasing their ability to solve problems in a diverse spectrum of applications such as the Biostatistics and Biology computer, Industrial Statistics, network reliability, etc ...

The term Statistics Algebra was coined by Pistone, Riccomagno and Wynn in 2001, in a context of applicability of computational algebraic techniques to Statistics. And the aim of Statistics Algebrawith is adapting originally characteristic of other areas for use techniques for solving problems of Statistics and its application to real situations.

Application to Information Theory

Considering algebras of random variables that appear naturally in the field of non-commutative probability, it could be tackled problems related to spectral theory, random matrix theory or quantum mechanics. Thus, in particular, the theory of random matrices, connected to the multivariate analysis, has recently taken a considerable significance with numerous applications in the design of models related to communication networks. More specifically, we highlight its application to information theory, areas of info-taxis (information-driven motion) and the biomolecular information theory.