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Exploration of geological variability and possible processes through the use of compositional data analysis: an example using scottish metamorphosed

Developments in the statistical analysis of compositional data over the last two decades have made possible a much deeper exploration of the nature of variability, and the possible processes associated with compositional data sets from many disciplines. In this paper we concentrate on geochemical data sets. First we explain how hypotheses of compositional variability may be formulated within the natural sample space, the unit simplex, including useful hypotheses of subcompositional discrimination and specific perturbational change. Then we develop through standard methodology, such as generalised likelihood ratio tests, statistical tools to allow the systematic investigation of a complete lattice of such hypotheses. Some of these tests are simple adaptations of existing multivariate tests but others require special construction. We comment on the use of graphical methods in compositional data analysis and on the ordination of specimens. The recent development of the concept of compositional processes is then explained together with the necessary tools for a staying- in-the-simplex approach, namely compositional singular value decompositions. All these statistical techniques are illustrated for a substantial compositional data set, consisting of 209 major-oxide and rare-element compositions of metamorphosed limestones from the Northeast and Central Highlands of Scotland. Finally we point out a number of unresolved problems in the statistical analysis of compositional processes

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

Manager: Thió i Fernández de Henestrosa, Santiago
Martín Fernández, Josep Antoni
Other contributions: Universitat de Girona. Departament d’Informàtica i Matemàtica Aplicada
Author: Thomas, C.W.
Aitchison, John
Date: 2003 October 16
Abstract: Developments in the statistical analysis of compositional data over the last two decades have made possible a much deeper exploration of the nature of variability, and the possible processes associated with compositional data sets from many disciplines. In this paper we concentrate on geochemical data sets. First we explain how hypotheses of compositional variability may be formulated within the natural sample space, the unit simplex, including useful hypotheses of subcompositional discrimination and specific perturbational change. Then we develop through standard methodology, such as generalised likelihood ratio tests, statistical tools to allow the systematic investigation of a complete lattice of such hypotheses. Some of these tests are simple adaptations of existing multivariate tests but others require special construction. We comment on the use of graphical methods in compositional data analysis and on the ordination of specimens. The recent development of the concept of compositional processes is then explained together with the necessary tools for a staying- in-the-simplex approach, namely compositional singular value decompositions. All these statistical techniques are illustrated for a substantial compositional data set, consisting of 209 major-oxide and rare-element compositions of metamorphosed limestones from the Northeast and Central Highlands of Scotland. Finally we point out a number of unresolved problems in the statistical analysis of compositional processes
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
Citation: Thomas, C.W.; Aitchison, J. ’Exploration of geological variability and possible processes through the use of compositional data analysis’ a CODAWORK’03. Girona: La Universitat, 2003 [consulta: 5 maig 2008]. Necessita Adobe Acrobat. Disponible a Internet a: http://hdl.handle.net/10256/673
ISBN: 84-8458-111-X
Document access: http://hdl.handle.net/10256/673
Language: eng
Publisher: Universitat de Girona. Departament d’Informàtica i Matemàtica Aplicada
Rights: Tots els drets reservats
Subject: Anàlisi multivariable
Geoquímica -- Mètodes estadístics
Title: Exploration of geological variability and possible processes through the use of compositional data analysis: an example using scottish metamorphosed
Type: info:eu-repo/semantics/conferenceObject
Repository: DUGiDocs

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