# The E-Posterior

arXiv: https://arxiv.org/abs/2301.01335 · HTML: https://mlsanity.com/paper/2301.01335/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jan 2023.

## Built on by (most cited first, 5 of 5)

- [Protected Test-Time Adaptation via Online Entropy Matching: A Betting Approach](https://mlsanity.com/paper/2408.07511/) (2024)
- [Improved Algorithms for Stochastic Linear Bandits Using Tail Bounds for Martingale Mixtures](https://mlsanity.com/paper/2309.14298/) (2023)
- [Fuzzy Prediction Sets: Conformal Prediction with E-values](https://mlsanity.com/paper/2509.13130/) (2025)
- [Meta-Analysis with Untrusted Data](https://mlsanity.com/paper/2407.09387/) (2024)
- [SLICE: Sequential Likelihood-Free Inference via Conformal E-Values](https://mlsanity.com/paper/2610.13855/) (2026)

## Abstract (arXiv)

We develop a representation of a decision maker's uncertainty based on e-variables. Like the Bayesian posterior, this *e-posterior* allows for making predictions against arbitrary loss functions that may not be specified ex ante. Unlike the Bayesian posterior, it provides risk bounds that have frequentist validity irrespective of prior adequacy: if the e-collection (which plays a role analogous to the Bayesian prior) is chosen badly, the bounds get loose rather than wrong, making *e-posterior minimax* decision rules safer than Bayesian ones. The resulting *quasi-conditional paradigm* is illustrated by re-interpreting a previous influential partial Bayes-frequentist unification, *Kiefer-Berger-Brown-Wolpert conditional frequentist tests*, in terms of e-posteriors.