Multivariate Bayesian semiparametric models for authentication of food and beverages

Food and beverage authentication is the process by which foods or beverages are verified as complying with its label description, for example, verifying if the denomination of origin of an olive oil bottle is correct or if the variety of a certain bottle of wine matches its label description. The common way to deal with an authentication process is to measure a number of attributes on samples of food and then use these as input for a classification problem. Our motivation stems from data consisting of measurements of nine chemical compounds denominated Anthocyanins, obtained from samples of Chilean red wines of grape varieties Cabernet Sauvignon, Merlot and Carm\'{e}n\`{e}re. We consider a model-based approach to authentication through a semiparametric multivariate hierarchical linear mixed model for the mean responses, and covariance matrices that are specific to the classification categories. Specifically, we propose a model of the ANOVA-DDP type, which takes advantage of the fact that the available covariates are discrete in nature. The results suggest that the model performs well compared to other parametric alternatives. This is also corroborated by application to simulated data.