Simplicial geometry for compositional data

By Juan José Egozcue, Vera Pawlowsky-Glahn. Geological Society Special Publication, 2006

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Imputation of missing values for compositional data using classical and robust methods (2010, background): “Principles on this geometry 3 were introduced in Aitchison (1986), and the resulting so-called Aitchison geometry holds the vector space as well as Hilbert space properties (see, e.g., Egozcue and Pawlowsky-Glahn, 2006).”
On the interpretation of differences between groups for compositional data (2015, background): “A reader interested in this topic will find a general description in Palarea-Albaladejo et al. (2014). Using a log-contrast one can define new variables (e.”
Rounded zeros: some practical aspects for compositional data (2006, methodology): “These techniques rely on fully parametric models for multivariate data, usually the normal distribution, and contain in their formulation the variance/covariance matrix. In view of the above arguments unreasonable results are likely to be obtained when classical methodology is applied to composition”
Bayesian-multiplicative treatment of count zeros in compositional data sets (2015, background): “In addition, the specific properties of CoDa induce their own geometry, the Aitchison geometry (e.g., Egozcue and Pawlowsky-Glahn, 2006), with the structure of a (D – 1)-dimensional Euclidean vector space.”