The difficult and ubiquitous problems of multiplicities

Area of Science:

• Statistics
• Data Analysis
• Scientific Inference

Background:

• Multiplicities, the occurrence of multiple statistical tests or analyses, are pervasive and can compromise the validity of research findings.
• Current statistical methodologies often focus on addressing known multiplicities, overlooking the more insidious impact of silent multiplicities.
• Underestimation of the importance of multiplicities by statisticians hinders robust data interpretation across various fields.

Purpose of the Study:

• To highlight the critical, yet often underestimated, importance of multiplicities in statistical inference.
• To emphasize the significance of addressing both known and silent multiplicities in research.
• To advocate for collaborative approaches between frequentist and Bayesian statisticians to tackle multiplicity issues.

Main Methods:

• Conceptual analysis of statistical inference in the presence of multiplicities.
• Discussion of the limitations of current methodologies for handling known multiplicities.
• Exploration of the challenges posed by silent multiplicities and the need for novel approaches.

Main Results:

• Identical experimental results can lead to divergent statistical conclusions due to unaddressed multiplicities.
• Standard software packages with default settings are insufficient for resolving all multiplicity problems.
• The importance of considering the unique aspects of each problem and the substantive area of application is underscored.

Conclusions:

• Addressing multiplicities, particularly silent ones, is crucial for accurate statistical inference.
• A collaborative effort between frequentist and Bayesian statistical paradigms offers a promising avenue for developing effective solutions.
• Context-specific understanding and tailored approaches are essential for managing multiplicities in any given research problem.