The central idea that unifies the Group is the statistical analysis of compositional data. In Geology, Petrology, Chemistry, Economics, Archaeometry, etc. we are used to work with vectors whose components represent relative parts of a whole. In fact, we are working with the mathematical foundations under the statistical analysis of this kind of data, and also with some of their wide-range applications.
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, disciminant, 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 algebric geometry to differential calculus in the simplex.
Furthermore, we are developing our own statistical package, the
due the total lack of a specific and user-friendly software intended to
treat compositional data.
Here you can view a video about the activity of the research group appeared on TV3(Televisió de Catalunya) (minute 2:08): Compositional data of the soil of Mercury