Correlation analysis for proportions via updating and resampling

Compositional data arise frequently in practice, but their statistical analysis is not yet well developed. Compositions arise when nonnegative random vectors are mapped into the unit simplex via a closure operation, e.g., when the amounts of certain minerals in a soil sample are converted to percentages. Components in random compositions can never be stochastically independent, due to the spurious correlation introduced by taking the closure of the basis vectors. This paper aims to assess independence of the unobserved basis vectors based on the observed composition. We propose a resampling procedure that is based on an updating formula. A simulation study shows that this procedure works well in the case, where the components of the composition are roughly of the same size. We apply the procedure to a geochemical data set obtained from the Kola peninsula.