Exact Selective Inference with Randomization

TL;DR

This paper presents a new exact selective inference method using a closed-form pivot based on a bivariate truncated Gaussian distribution, improving confidence interval precision in Gaussian models despite some power trade-offs.

Contribution

It introduces a novel pivot for exact selective inference with randomization, simplifying the inference process and providing narrower confidence intervals than existing data splitting methods.

Findings

The pivot achieves exact inference in Gaussian regression models.

Narrower confidence intervals compared to data splitting.

Trade-off between power and exactness demonstrated on datasets.

Abstract

We introduce a pivot for exact selective inference with randomization. Not only does our pivot lead to exact inference in Gaussian regression models, but it is also available in closed form. We reduce the problem of exact selective inference to a bivariate truncated Gaussian distribution. By doing so, we give up some power that is achieved with approximate maximum likelihood estimation in Panigrahi and Taylor (2022). Yet our pivot always produces narrower confidence intervals than a closely related data splitting procedure. We investigate the trade-off between power and exact selective inference on simulated datasets and an HIV drug resistance dataset.