A scale-only nonparametric mixture model for clustering covariance matrices: an application to olive oil chemical profiles

Understanding how dependence structures vary across groups is a fundamental problem in multivariate analysis. When observations are naturally organized into distinct groups, a key objective is to determine whether these groups share similar covariance patterns or exhibit structurally different relationships among variables. We consider a dataset comprising chemical measurements of the acid components of olive oil samples produced in different regions of Italy. Our goal is to assess whether oils from different regions display similar or distinct profiles of interdependence among variables. To address this problem, we introduce a Bayesian nonparametric scale-only mixture model for clustering covariance matrices. We focus on the setting in which the outcome of interest is reasonably modeled by a multivariate Gaussian distribution. By leveraging conjugate priors, we enable inference to be performed exactly, without resorting to approximations or computational strategies.