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