Position: There Is No Free Bayesian Uncertainty Quantification

Ivan Melev; Goeran Kauermann

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arXiv · 2506.03670

Position: There Is No Free Bayesian Uncertainty Quantification

Ivan Melev·Goeran Kauermann

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Abstract

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.

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Ivan Melev, Goeran Kauermann. 2025-06-04. Position: There Is No Free Bayesian Uncertainty Quantification. https://arxiv.org/abs/2506.03670

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