Statistical Analysis of Compositional Data

Description of impact

We are working with the mathematical foundations under the statistical analysis of compositional data. From the vast workings of professor J. Aitchison in this field, built up from a statistical point of view since the early eighties, we have seen that rigorous mathematical foundations are needed to properly understand and apply these techniques. We base them in the definition of a geometric structure for the Simplex (the support space of compositional data). Afterwards, traditional statistical techniques (cluster, discriminant, factor analysis, regression models, etc.) are being adapted to this structure: we are covering both their real-case application and theoretical development, from measure theory or algebraic geometry to differential calculus in the simplex.