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Objectives and General Information
Introduction:
A short course on compositional data analysis will be given on the afternoons of one week (mon-fri) on July 2010, at the premises of the Technical University of Catalonia (UPC), in Barcelona.
Objective:
To provide an introduction to the theoretical and practical aspects of statistical analysis of compositional data, as well as an informal discussion forum on more advanced modelling topics.
Contents:
Compositional data are vectors which components show the relative importance of some parts of a whole. Typical examples are data presented in percentages, ppm, ppb, or the like. Aitchison introduced the log-ratio approach to analyse CoDa back in the eighties. Since then, progress has been done in understanding the geometry peculiar to their sample space, the D-part simplex. This course will present the current state of the art in this field of active research and will cover the following topics:
- Hypothesis underlying statistical data analysis (sample space, scale).
- The Aitchison geometry of the simplex.
- Coordinate representation; distributions on the simplex.
- Exploratory analysis (centering, variation array, biplot, balances-dendrogram).
- Linear processes in the simplex; regression.
- Introduction to multivariate analysis: cluster and discriminant
- Introduction to available software.
- Open discussion session: bring your own data!
Recommended background:
First semester courses in statistics, algebra and calculus; basic knowledge in multivariate statistics
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