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- Gregory B. Gloor, Jia Wu, Vera Pawlowsky-Glahn, Juan José Egozcue
- Annals of epidemiology
- 2016

PURPOSE
The ability to properly analyze and interpret large microbiome data sets has lagged behind our ability to acquire such data sets from environmental or clinical samples. Sequencing instruments impose a structure on these data: the natural sample space of a 16S rRNA gene sequencing data set is a simplex, which is a part of real space that is… (More)

- David Lovell, Vera Pawlowsky-Glahn, Juan José Egozcue, Samuel Marguerat, Jürg Bähler
- PLoS Computational Biology
- 2015

In the life sciences, many measurement methods yield only the relative abundances of different components in a sample. With such relative-or compositional-data, differential expression needs careful interpretation, and correlation-a statistical workhorse for analyzing pairwise relationships-is an inappropriate measure of association. Using yeast gene… (More)

Abstract: Within the special geometry of the simplex, the sample space of compositional data, compositional orthonormal coordinates allow the application of any multivariate statistical approach. The search for meaningful coordinates has suggested balances (between two groups of parts)—based on a sequential binary partition of a D-part composition—and a… (More)

Regression models with compositional response have been studied from the beginning of the log-ratio approach for analysing compositional data. These early approaches suggested the statistical hypothesis of logistic-normality of the compositional residuals to test the model and its coefficients. Also, the Dirichlet distribution has been proposed as an… (More)

- Xavier Quintana, Sandra Brucet, +6 authors Juan José Egozcue
- 2008

The most suitable method for estimation of size diversity is investigated. Size diversity is computed on the basis of the Shannon diversity expression adapted for continuous variables, such as size. It takes the form of an integral involving the probability density function (pdf) of the size of the individuals. Different approaches for the estimation of pdf… (More)

We propose a general approach to deal with nonlinear, nonconvex variational problems based on a reformulation of the problem resulting in an optimization problem with linear cost functional and convex constraints. As a first step we explicitly explore these ideas to some one-dimensional variational problems and obtain specific conclusions of an analytical… (More)

Under the assumption that the Aitchison geometry holds in the simplex, standard analysis of compositional data assumes a uniform distribution as reference measure of the space. Changing the reference measure induces a weighting of parts. The changes that appear in the algebraic-geometric structure of the simplex are analysed, as a step towards understanding… (More)

- Serge-Étienne Parent, Léon Etienne Parent, +10 authors William Natale
- Front. Plant Sci.
- 2013

Tissue analysis is commonly used in ecology and agronomy to portray plant nutrient signatures. Nutrient concentration data, or ionomes, belongs to the compositional data class, i.e., multivariate data that are proportions of some whole, hence carrying important numerical properties. Statistics computed across raw or ordinary log-transformed nutrient data… (More)

Phenomena with a constrained sample space appear frequently in practice. This is the case, for example, with strictly positive data, or with compositional data, such as percentages or proportions. If the natural measure of difference is not the absolute one, simple algebraic properties show that it is more convenient to work with a geometry different from… (More)

- José Luis Díaz-Barrero, Juan José Egozcue
- Appl. Math. Lett.
- 2004