Gaussian discriminant analysis is a popular classification model, that in the precise case can produce unreliable predictions in case of high uncertainty (scarce or noisy data set). While imprecise probability theory offer a nice theoretical framework to solve such issues, it has not been yet applied to Gaussian discriminant analysis. This work remedies this, by proposing a new Gaussian discriminant analysis based on robust Bayesian analysis and near-ignorance priors. The model delivers cautious predictions, in form of set-valued class, in case of limited or imperfect available information. Experiments show that including an imprecise component in the Gaussian discriminant analysis produce reasonably cautious predictions, and that set-valued predictions correspond to instances for which the precise model performs poorly.