# Post-Hoc Large-Sample Statistical Inference

arXiv: https://arxiv.org/abs/2603.08002 · HTML: https://mlsanity.com/paper/2603.08002/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Mar 2026.

## Built on by (most cited first, 4 of 4)

- [Post-Selection Distributional Model Evaluation](https://mlsanity.com/paper/2603.23055/) (2026)
- [Optimizing Social Utility in Sequential Experiments](https://mlsanity.com/paper/2605.06520/) (2026)
- [Bentkus-type asymptotic e-values](https://mlsanity.com/paper/2606.06332/) (2026)
- [Confidence Horizons](https://mlsanity.com/paper/2608.03889/) (2026)

## Abstract (arXiv)

We derive inferential procedures for large sample sizes that remain valid under data-dependent significance levels (so-called "post-hoc valid inference"). Classical statistical tools require that the significance level -- the "type-I error" -- is selected prior to seeing or analyzing any data. This restriction leads to some drawbacks. For instance, if an analyst generates an inconclusive confidence interval, repeating the process with a larger significance level is not an option -- the result is final. Recently, e-values have emerged as the solution to this problem, being both necessary and sufficient tools for performing various forms of post-hoc inference. All such results, however, have thus far been nonasymptotic. As a result, they inherit familiar limitations of nonasymptotic inferential procedures such as requiring strong moment assumptions and being conservative in general. This paper develops a theory of post-hoc inference in the asymptotic setting, yielding asymptotic post-hoc confidence sets and asymptotic post-hoc p-values that make weaker assumptions and are sharper than their nonasymptotic counterparts.