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Beyond Neyman-Pearson: E-values enable hypothesis testing with a data-driven alpha.

Peter D Grünwald1,2

  • 1Machine Learning Group, National research institute for mathematics and computer science in the Netherlands (Centrum Wiskunde & Informatica), Amsterdam 1098 XG, The Netherlands.

Proceedings of the National Academy of Sciences of the United States of America
|September 20, 2024
PubMed
Summary
This summary is machine-generated.

The study introduces e-values as a superior alternative to P-values in statistical hypothesis testing. E-values offer better decision-making, especially with extreme data, and provide robust risk control for both Type-I and Type-II errors.

Keywords:
confidencedecision theorye-valuesevidencehypothesis testing

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Area of Science:

  • Statistics
  • Statistical Hypothesis Testing

Background:

  • Traditional hypothesis testing relies on P-values, which have limitations in decision-making with extreme observations.
  • Current methods lack clear guidance for optimizing frequentist decisions post-data observation.

Purpose of the Study:

  • To demonstrate the advantages of using e-values over P-values in statistical hypothesis testing.
  • To highlight how e-values facilitate better decision-making and risk control in a post hoc setting.

Main Methods:

  • The study proposes and analyzes the use of e-values within a generalized Neyman-Pearson framework.
  • It explores e-value-based decision rules for controlling Type-I and Type-II risks.
  • The research extends the application to e-confidence sets and e-posteriors for valid risk guarantees.

Main Results:

  • E-values provide straightforward Type-I risk control and enable better frequentist decisions, especially with extreme data.
  • In post hoc settings considering Type-II risks, e-value-based rules are the only admissible decision rules.
  • E-confidence sets and e-posteriors offer valid risk guarantees when loss functions are not fixed in advance.

Conclusions:

  • E-values represent a significant advancement over P-values for statistical hypothesis testing and decision-making.
  • Their application ensures valid risk control in diverse scenarios, including post hoc analysis and when loss functions are flexible.
  • Further development and deployment of e-values are crucial for broader adoption in statistical practice.