Session 1: Geometry and statistics in the simplexhttp://hdl.handle.net/10256/6202015-08-05T07:42:51Z2015-08-05T07:42:51ZWhen a data set can be considered compositional?Barceló i Vidal, Carleshttp://hdl.handle.net/10256/6512012-06-28T12:30:36Z2003-10-15T00:00:00ZWhen a data set can be considered compositional?
Barceló i Vidal, Carles
Thió i Fernández de Henestrosa, Santiago; Martín Fernández, Josep Antoni
Traditionally, compositional data has been identified with closed data, and the simplex has been considered as the natural sample space of this kind of data. In our opinion, the emphasis on the constrained nature of
compositional data has contributed to mask its real nature. More crucial than the constraining property of compositional data is the scale-invariant property of this kind of data. Indeed, when we are considering only few parts of a full composition we are not working with constrained data but our data are still compositional. We believe that it is necessary to give a more precise
definition of composition. This is the aim of this oral contribution
2003-10-15T00:00:00ZDistributions on the simplexMateu i Figueras, GlòriaPawlowsky-Glahn, VeraBarceló i Vidal, Carleshttp://hdl.handle.net/10256/6502012-06-28T12:30:36Z2003-10-15T00:00:00ZDistributions on the simplex
Mateu i Figueras, Glòria; Pawlowsky-Glahn, Vera; Barceló i Vidal, Carles
Thió i Fernández de Henestrosa, Santiago; Martín Fernández, Josep Antoni
The simplex, the sample space of compositional data, can be structured as a real Euclidean space. This fact allows to work with the coefficients with respect to an orthonormal basis. Over these coefficients we apply standard real analysis, inparticular, we define two different laws of probability trought the density function and we study their main properties
2003-10-15T00:00:00ZHilbert space on probability density functions with Aitchison geometryEgozcue, Juan JoséDíaz Barrero, José Luishttp://hdl.handle.net/10256/6492012-06-28T12:30:36Z2003-10-15T00:00:00ZHilbert space on probability density functions with Aitchison geometry
Egozcue, Juan José; Díaz Barrero, José Luis
Thió i Fernández de Henestrosa, Santiago; Martín Fernández, Josep Antoni
Compositional data analysis motivated the introduction of a complete Euclidean structure in the simplex of D parts. This was based on the early work of J. Aitchison (1986) and completed recently when Aitchinson distance in the simplex was associated with an inner product and orthonormal bases were identified (Aitchison and others, 2002; Egozcue and others, 2003). A partition of the support of a random variable generates a composition by assigning the probability of each interval to a part of the composition. One can imagine that the partition can be refined and the probability density would represent a kind of continuous composition of probabilities in a simplex of infinitely many parts. This intuitive idea would lead to a Hilbert-space of probability densities
by generalizing the Aitchison geometry for compositions in the simplex into the set probability densities
2003-10-15T00:00:00ZStatistical modeling on coordinatesPawlowsky-Glahn, Verahttp://hdl.handle.net/10256/6482012-06-28T12:30:36Z2003-10-15T00:00:00ZStatistical modeling on coordinates
Pawlowsky-Glahn, Vera
Thió i Fernández de Henestrosa, Santiago; Martín Fernández, Josep Antoni
This paper is a first draft of the principle of statistical modelling on coordinates. Several causes —which would be long to detail—have led to this situation close to the deadline for submitting papers to CODAWORK’03. The main of them is the fast development of the approach along the
last months, which let appear previous drafts as obsolete. The present paper contains the essential parts of the state of the art of this approach from my point of view. I would like to acknowledge many clarifying discussions with the group of people working in this field in Girona, Barcelona, Carrick Castle, Firenze, Berlin, G¨ottingen, and Freiberg. They have given a lot of suggestions and ideas. Nevertheless, there might be still errors or unclear aspects which are exclusively my fault. I hope this contribution serves as a basis for further discussions and new developments
2003-10-15T00:00:00Z