Keynote speakers

Kamila Fačevicová

Kamila Fačevicová is an Assistant Professor at Palacký University Olomouc, Czech Republic. She reached her Ph.D. in 2016 and within her thesis she focused on coordinate representation of two-factorial compositional data – compositional tables. Nowadays she dedicates the main part of her research interest to the study of the geometric structure and properties of multi-factorial compositional data. Compositional tables, as well as multi-factorial compositional data, represent a natural extension of the traditional concept of vector compositional data. It turns out that a better understanding of their structure opens the door to the development of a new family of compositional methods focusing on relations between the constituting variables. Besides this main topic, she is also active in applied research, ranging from medicine or politology to geochemistry. Within these applications, she combines compositional, robust and classical approaches to the data analysis, what also helps to reveal new topics for theoretical developments. An important part of her academic life belongs to teaching and work with students, when she helps, together with her colleagues, to grow up a new generation of (compositional) statisticians.

Raimon Tolosana-Delgado

Raimon is a senior scientist at the Helmholtz Institute Freiberg for Resource Technology (Helmholtz-Zentrum Dresden-Rossendorf). He studied Engineering Geology at the Tehnical University of Catalunya and the Universiy of Barcelona, and completed his PhD at the University of Girona. Ever since his diploma thesis he has been working in applications of compositional data analysis in geology, environmental sciences, and geo-engineering, most particularly in sedimentology, ore geology and mining. He holds the Felix Chayes Prize of the International Association of Mathematical Geosciences for his research on these topics. His areas of interest cover, additionally to compositional data analysis, geostatistics, model-data integration, predictive geometallurgy, Bayesian statistics and R programming.

Analysis of multi-factorial compositional data: what we already know and where we are heading

Compositional data are in their traditional setting understood as vector observations of positive entries. This means, that the observations carry an information about the relative structure given by the values of one factor. The contribution will focus on a more complex situation where the structure is given by two or more determining factors. The two-factorial case is already thoroughly described in literature and can be found under the key word compositional tables. It turns out that the main findings about the geometrical structure of tables and their coordinate representation can be further extended to the multi-factorial case. The presentation brings an overview of the current state of knowledge in the field of analysis of multi-factorial compositional data. The theoretical principles will be followed by practical examples, demonstrating the treatment of multi-factorial compositions in the framework of (robust) principle component analysis or analysis of spatial or time dependent data. Finally, perspectives of the further research in the field will be discussed.

Geostatistics for compositional data: from spatial interpolation to high dimensional prediction

Geostatistics is a name given to a series of statistical and machine learning tools devised to treat a spatially dependent variable with the goal of interpolating it. The key tool of classical geostatistics is the covariance function, capturing the covariance (matrix) between the variable (vector) observed at two locations in space. Pawlowsky-Glahn and Olea (2004; "Geostatistical analysis for compositional data") already extended this framework to deal with spatially dependent compositional data, taking a logratio transformation, i.e. by means of the covariance function of the logratio transformed scores. Given a spatially dependent compositional data set, if we had available a model for the covariance function, it would be possible to predict the composition at a new location by means of multivariate multiple linear regression. The typical approach to obtain this covariance is to restrict it to be location-independent (but still depend on the lag difference between locations), and give it a parametric form. This vector of parameters is then either fitted via maximum likelihood, or else data-driven to specific collections of spread statistics of the sample. Similar approaches can be followed with compositions. Several such data driven methods have been proposed for compositions, which can be seen as choosing an oblique logratio such that the covariance function becomes a diagonal matrix for all lags (and by extension, for all pairs of locations), with the resulting diagonal elements easily modelled separately. In this contribution we will discuss the several implications of these methodologies to obtain a parametric model for the covariance function, how to use this function to predict the composition at any location, the subcompositional properties of this predictor, and how this whole framework can be used beyond spatial statistics, to establish (almost) non-parametric predictive models for compositional responses with high dimensional regressors.