B0781
Title: Algebraic statistics for data carrying relative, rather than absolute, information
Authors: Francesco Porro - Universita degli Studi di Genova (Italy) [presenting]
Eva Riccomagno - Università degli Studi di Genova (Italy)
Abstract: In recent years, there has been a renewed interest in the analysis of compositional data (CoDa), motivated by different applications in several fields. A compositional data point is characterized by a constant-sum constraint on the sample values, for example, percentages or proportions. They are specifically designed to analyze the distribution of a whole and the relative importance of the constituent parts. When the constant constraint is on the controlled factors, one can talk of so-called mixture experiments. The twenty-century literature provides standard mixture designs for fitting standard regression models, such as simplex-lattice designs and simplex-centroid designs. There are papers in algebraic statistics (AS) that address the issue of planning an experiment for compositional factors starting from the standard setup. These are not fully exploited and not fully integrated with the CoDa setup. The AS approach is reviewed and its theoretical limitations are highlighted for the applications of current interest, as well as investigate ways to overcome them.
