# Inference conditional on selection: a review

arXiv: https://arxiv.org/abs/2604.09779 · HTML: https://mlsanity.com/paper/2604.09779/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Apr 2026.

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

- [How Sensitive Are LLM Leaderboard Claims to Hidden Model Selection?](https://mlsanity.com/paper/2609.28177/) (2026)
- [Selective Inference for Clustering Under Unknown Covariance](https://mlsanity.com/paper/2610.17458/) (2026)

## Abstract (arXiv)

In this article, we review selective inference, a set of techniques for inference when the statistical question asked is a function of the data. This setting often arises in contemporary scientific workflows, where hypotheses and parameters may be selected from the data, rather than specified in advance. In this setting, classical inferential techniques do not achieve "classical" guarantees, such as nominal coverage of confidence intervals. We consider three examples for which selective inference solutions are required: inference on a "winner", inference on the mean of a region in a regression tree, and inference on the difference in means between a pair of clusters. We argue that conditional guarantees are of scientific interest in such settings. We then review and draw connections between several approaches that provide such guarantees. Finally, we illustrate these approaches in simulation and through an application to single-cell RNA sequencing data.