Uma análise bayesiana para dados composicionais

Abstract

Compositional data are given by vectors of positive numbers with sum equals to one. These kinds of data are common in many applications, as in geology, biology, economy among many others. In this paper, we introduce a Bayesian analysis for compositional data considering additive log-ratio (ALR) and Box-Cox transformations assuming a mul- tivariate normal distribution for correlated errors. These results generalize some existing Bayesian approaches assuming uncorrelated errors. We also consider the use of expo- nential power distributions for uncorrelated errors considering additive log-ratio (ALR) transformation. We illustrate the proposed methodology considering a real data set.