Selective inference is easier with p-values

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Contributed Abstract 

Paper 

Anav Sood (1)

(1) Stanford University, N/A

Anav Sood  
Stanford University

Anav Sood  
Stanford University

Selective inference is a subfield of statistics that enables valid inference after selection of a data-dependent question. In this paper, we introduce selectively dominant p-values, a class of p-values that allow practitioners to easily perform inference after arbitrary selection procedures. Unlike a traditional p-value, whose distribution must stochastically dominate the uniform distribution under the null, a selectively dominant p-value must have a post-selection distribution that stochastically dominates that of a uniform having undergone the same selection process; moreover, this property must hold simultaneously for all possible selection processes. Despite the strength of this condition, we show that all commonly used p-values are selectively dominant. By recasting two canonical selective inference problems-inference on winners and rank verification-in our selective dominance framework, we provide simpler derivations, a deeper conceptual understanding, and new generalizations and variations of these methods. Additionally, we use our insights to introduce selective variants of methods that combine p-values, such as Fisher's combination test.

Selective inference|Winner's curse|Rank Verification|Publication bias|Data carving |Conditional inference

IMS

Statistical Methodology