Integrative methods for post-selection inference under convex constraints

Snigdha Panigrahi, Jonathan Taylor, Asaf Weinstein

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

Inference after model selection has been an active research topic in the past few years, with numerous works offering different approaches to addressing the perils of the reuse of data. In particular, major progress has been made recently on large and useful classes of problems by harnessing general theory of hypothesis testing in exponential families, but these methods have their limitations. Perhaps most immediate is the gap between theory and practice: implementing the exact theoretical prescription in realistic situations—for example, when new data arrives and inference needs to be adjusted accordingly—may be a prohibitive task. In this paper, we propose a Bayesian framework for carrying out inference after variable selection. Our framework is very flexible in the sense that it naturally accommodates different models for the data instead of requiring a case-by-case treatment. This flexibility is achieved by considering the full selective likelihood function where, crucially, we propose a novel and nontrivial approximation to the exact but intractable expression. The advantages of our methods in practical data analysis are demonstrated in an application to HIV drug-resistance data.

Original languageAmerican English
Pages (from-to)2803-2824
Number of pages22
JournalAnnals of Statistics
Volume49
Issue number5
DOIs
StatePublished - Oct 2021

Bibliographical note

Publisher Copyright:
© Institute of Mathematical Statistics, 2021.

Keywords

  • Adaptive data analysis
  • Bayesian inference
  • Carving
  • Conditional inference
  • Convex constraints
  • Selective inference

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