Position: There Is No Free Bayesian Uncertainty Quantification

Due to their intuitive appeal, Bayesian methods of modeling and uncertainty quantification have become popular in modern machine and deep learning. When providing a prior distribution over the parameter space, it is straightforward to obtain a distribution over the parameters that is conventionally interpreted as uncertainty quantification of the model. We challenge the validity of such Bayesian uncertainty quantification by discussing the equivalent optimization-based representation of Bayesian updating, provide an alternative interpretation that is coherent with the optimization-based perspective, propose measures of the quality of the Bayesian inferential stage, and suggest directions for future work.

@article{melev2025_2506.03670,
  title={ Position: There Is No Free Bayesian Uncertainty Quantification },
  author={ Ivan Melev and Goeran Kauermann },
  journal={arXiv preprint arXiv:2506.03670},
  year={ 2025 }
}