  Several recent works encourage the use of a Bayesian framework when assessing
performance and fairness metrics of a classification algorithm in a supervised
setting. We propose the Uncertainty Matters (UM) framework that generalizes a
Beta-Binomial approach to derive the posterior distribution of any criteria
combination, allowing stable performance assessment in a bias-aware setting.We
suggest modeling the confusion matrix of each demographic group using a
Multinomial distribution updated through a Bayesian procedure. We extend UM to
be applicable under the popular K-fold cross-validation procedure. Experiments
highlight the benefits of UM over classical evaluation frameworks regarding
informativeness and stability.
