Objective Bayesian analysis for the normal compositional model

The issue of objective prior specification for the parameters in the normal compositional model is considered within the context of statistical analysis of linearly mixed structures in image processing. In particular, the Jeffreys prior for the vector of fractional abundances in case of a known covariance matrix is derived. If an additional unknown variance parameter is present, the Jeffreys prior and the reference prior are computed and it is proven that the resulting posterior distributions are proper. Markov chain Monte Carlo strategies are proposed to efficiently sample from the posterior distributions and the priors are compared on the grounds of the frequentist properties of the resulting Bayesian inferences. The default Bayesian analysis is illustrated by a dataset taken from fluorescence spectroscopy.