Sampling models for selective inference
File(s)
Accepted version
Author(s)
García Rasines, Daniel
Young, G Alastair
Type
Journal Article
Abstract
This paper explores the challenges of constructing suitable inferential models in scenarios where the parameter of interest is determined in light of the data, such as regression after variable selection. Two compelling arguments for conditioning converge in this context, whose interplay can introduce ambiguity in the choice of conditioning strategy: the Conditionality Principle, from classical statistics, and the ‘condition on selection’ paradigm, central to selective inference. We discuss two general principles that can be employed to resolve this ambiguity in some recurrent contexts. The first one refers to the consideration of how information is processed at the selection stage. The second one concerns an exploration of ancillarity in the presence of selection. We demonstrate that certain notions of ancillarity are preserved after conditioning on the selection event, supporting the application of the Conditionality Principle. We illustrate these concepts through examples and provide guidance on the adequate inferential approach in some common scenarios.
Date Issued
2025-07-21
Date Acceptance
2025-07-06
Citation
Sankhya A, 2025
ISSN
0976-836X
Publisher
Springer Science and Business Media LLC
Journal / Book Title
Sankhya A
Copyright Statement
Copyright © 2025, Indian Statistical Institute. This is the author’s accepted manuscript made available under a CC-BY licence in accordance with Imperial’s Research Publications Open Access policy (www.imperial.ac.uk/oa-policy)
License URL
Publication Status
Published online
Date Publish Online
2025-07-21