# Confidence sequences with informative, bounded-influence priors

arXiv: https://arxiv.org/abs/2506.22925 · HTML: https://mlsanity.com/paper/2506.22925/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jun 2025.

## Built on by (most cited first, 2 of 2)

- [Asymptotically Log-Optimal Bayes-Assisted Confidence Sequences for Bounded Means](https://mlsanity.com/paper/2605.07964/) (2026)
- [Confidence Horizons](https://mlsanity.com/paper/2608.03889/) (2026)

## Abstract (arXiv)

Confidence sequences are collections of confidence regions that simultaneously cover the true parameter for every sample size at a prescribed confidence level. Tightening these sequences is of practical interest and can be achieved by incorporating prior information through the method of mixture martingales. However, confidence sequences built from informative priors are vulnerable to misspecification and may become vacuous when the prior is poorly chosen. We study this trade-off for Gaussian observations with known variance. By combining the method of mixtures with a global informative prior whose tails are polynomial or exponential and the extended Ville's inequality, we construct confidence sequences that are sharper than their non-informative counterparts whenever the prior is well specified, yet remain bounded under arbitrary misspecification. The theory is illustrated with several classical priors.