Title: A journey of the Dirichlet distribution in the analysis of compositional data sets
Authors: Seitebaleng Makgai - University of Pretoria (South Africa) [presenting]
Abstract: Data sets that consist of proportions (and thus subject to unit-sum constraints) are known as compositional data sets. These types of data sets naturally arise in a variety of disciplines, such as the medical sciences, biology, as well as in psychology. The Dirichlet distribution is a well-known candidate in modelling compositional data sets. However, in the presence of some extreme points or outliers, the Dirichlet distribution fails to model such data sets, making other model extensions necessary. As a solution to this shortfall, a technique called the beta-generating technique is applied in developing Dirichlet-type distributions that present greater flexibility in modelling various compositional data sets in the medical and biological sciences. These developments result in the proposal of the Dirichlet-Gamma distribution. As part of the study, the performance of the Dirichlet-Gamma distribution is investigated in a Bayesian context. The usefulness of this model is demonstrated through the application of a real data set in the medical and biological sciences.