Ítem


Hilbert space on probability density functions with Aitchison geometry

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

Geologische Vereinigung; Universitat de Barcelona, Equip de Recerca Arqueomètrica; Institut d’Estadística de Catalunya; International Association for Mathematical Geology; Patronat de l’Escola Politècnica Superior de la Universitat de Girona; Fundació privada: Girona, Universitat i Futur.

Universitat de Girona. Departament d’Informàtica i Matemàtica Aplicada

Director: Thió i Fernández de Henestrosa, Santiago
Martín Fernández, Josep Antoni
Altres contribucions: Universitat de Girona. Departament d’Informàtica i Matemàtica Aplicada
Autor: Egozcue, Juan José
Díaz Barrero, José Luis
Data: 15 octubre 2003
Resum: 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
Geologische Vereinigung; Universitat de Barcelona, Equip de Recerca Arqueomètrica; Institut d’Estadística de Catalunya; International Association for Mathematical Geology; Patronat de l’Escola Politècnica Superior de la Universitat de Girona; Fundació privada: Girona, Universitat i Futur.
Format: application/pdf
Cita: Egozcue, J.J.; Díaz Barrero, J.L. ’Hilbert space on probability density functions with Aitchison geometry’ a CODAWORK’03. Girona: La Universitat, 2003 [consulta: 2 maig 2008]. Necessita Adobe Acrobat. Disponible a Internet a: http://hdl.handle.net/10256/649
ISBN: 84-8458-111-X
Accés al document: http://hdl.handle.net/10256/649
Llenguatge: eng
Editor: Universitat de Girona. Departament d’Informàtica i Matemàtica Aplicada
Drets: Tots els drets reservats
Matèria: Hilbert, Àlgebra de
Anàlisi funcional
Títol: Hilbert space on probability density functions with Aitchison geometry
Tipus: info:eu-repo/semantics/conferenceObject
Repositori: DUGiDocs

Matèries

Autors