Inference conditional on selection: a review

TL;DR

This review discusses selective inference techniques for data-dependent hypotheses, emphasizing their importance in scientific workflows and illustrating their application through examples and simulations.

Contribution

It provides a comprehensive overview of methods for inference after data-driven selection, highlighting their scientific relevance and connecting various approaches.

Findings

Conditional guarantees are scientifically valuable in data-dependent inference.

Selected examples demonstrate the application of selective inference methods.

Simulations and real data illustrate the effectiveness of these techniques.

Abstract

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.