Appendix for On Uncertainty, Tempering, and Data Augmentation in Bayesian Classification

Overall, properly representing aleatoric uncertainty is a challenging but fundamentally important consideration in Bayesian classification. We have shown that posterior tempering provides a mechanism to more honestly represent our beliefs about aleatoric uncertainty, especially in the presence of data augmentation. In general, as in Wilson and Izmailov [ 62 ], we should not be alarmed if T =1 is not optimal in sophisticated models on complex real-world datasets. Moreover, we have shown how other mechanisms to represent aleatoric uncertainty, such as the noisy Dirichlet model, 17 do not suffer from a cold posterior effect in the presence of data augmentation. Indeed, while an interesting phenomenon, cold posteriors should not be conflated with the success or failure of Bayesian deep learning.