# Position: There Is No Free Bayesian Uncertainty Quantification

arXiv: https://arxiv.org/abs/2506.03670 · HTML: https://mlsanity.com/paper/2506.03670/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 27 references that are in the map.
- First posted on arXiv 4 Jun 2025.

## Builds on (most cited first, 11 of 11)

- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [Being Bayesian, Even Just a Bit, Fixes Overconfidence in ReLU Networks](https://mlsanity.com/paper/2002.10118/) (2020)
- [A Primer on PAC-Bayesian Learning](https://mlsanity.com/paper/1901.05353/) (2019)
- [Concentration of tempered posteriors and of their variational approximations](https://mlsanity.com/paper/1706.09293/) (2017)
- [PAC Confidence Sets for Deep Neural Networks via Calibrated Prediction](https://mlsanity.com/paper/2001.00106/) (2019)
- [Minimum Description Length Revisited](https://mlsanity.com/paper/1908.08484/) (2019)
- [PAC Confidence Predictions for Deep Neural Network Classifiers](https://mlsanity.com/paper/2011.00716/) (2020)
- [Towards Efficient MCMC Sampling in Bayesian Neural Networks by Exploiting Symmetry](https://mlsanity.com/paper/2304.02902/) (2023)
- [Bayesian graph convolutional neural networks via tempered MCMC](https://mlsanity.com/paper/2104.08438/) (2021)
- [Bayesian neural networks via MCMC: a Python-based tutorial](https://mlsanity.com/paper/2304.02595/) (2023)
- [A Tight Excess Risk Bound via a Unified PAC-Bayesian-Rademacher-Shtarkov-MDL Complexity](https://mlsanity.com/paper/1710.07732/) (2017)

## Abstract (arXiv)

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.