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A decision theoretic approach to optimization of multiple testing procedures.

Vera Lisovskaja1, Carl-Fredrik Burman

  • 1Department of Mathematical Sciences, Chalmers University of Technology and Göteborg University, SE-412 96, Göteborg, Sweden.

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|November 14, 2014
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Summary
This summary is machine-generated.

This study optimizes multiple testing procedures (MTPs) using a utility function. Numerical methods calculate expected utility, revealing gains from optimized Bonferroni-based procedures like Holm and gatekeeping methods.

Keywords:
Closed testsMultiplicityRecyclingUtility

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Area of Science:

  • Statistics
  • Statistical inference
  • Multiple hypothesis testing

Background:

  • Multiple testing procedures (MTPs) are crucial for controlling errors in statistical inference.
  • Bonferroni-based closed testing procedures are widely used but may not be optimal for specific goals.
  • Optimizing MTPs based on a utility function can enhance decision-making power.

Purpose of the Study:

  • To develop and evaluate methods for optimizing multiple testing procedures (MTPs).
  • To investigate the performance of optimized Bonferroni-based closed testing procedures.
  • To quantify the gains achieved by optimizing MTPs with respect to a utility function.

Main Methods:

  • Focus on Bonferroni-based closed testing procedures, including Holm, fallback, gatekeeping, and graphical methods.
  • Development of numerical algorithms for calculating the expected utility of MTPs.
  • Comparative analysis of optimized procedures against standard ones using illustrative examples.

Main Results:

  • Optimal procedures were derived by maximizing a predefined utility function.
  • Numerical algorithms provide a practical way to compute expected utility for complex MTPs.
  • Significant gains in utility were demonstrated through optimization in various scenarios.

Conclusions:

  • Optimizing MTPs with respect to a utility function leads to improved statistical decision-making.
  • Bonferroni-based closed testing procedures can be effectively optimized for enhanced performance.
  • The proposed methods offer a valuable framework for selecting and tailoring MTPs in scientific research.