Testing multiple hypotheses with skewed alternatives.

Area of Science:

• Statistics
• Biostatistics
• Bioinformatics

Background:

• Multiple hypothesis testing often assumes symmetric alternative distributions, which may not reflect real-world data.
• Skewed distributions in alternatives are common in practical applications, yet often overlooked in standard testing procedures.
• Existing methods may lack power when dealing with non-symmetric alternative distributions.

Purpose of the Study:

• To develop a Bayesian decision theoretic rule for multiple directional hypothesis testing.
• To leverage prior knowledge of skewed alternative distributions for increased statistical power.
• To control a mixed directional false discovery rate under skewed alternatives.

Main Methods:

• A Bayesian decision rule was formulated for directional hypothesis testing with skewed alternatives.
• The proposed Bayesian method was compared against the frequentist Benjamini-Yekutieli rule.
• Simulations were conducted to evaluate the power and performance of the proposed rule.
• The method was applied to a real-world HIV dataset for validation.

Main Results:

• The proposed Bayesian rule demonstrated higher power compared to procedures assuming symmetric alternatives.
• The method effectively controlled the mixed directional false discovery rate under skewed distributions.
• Simulations confirmed the superior performance of the Bayesian approach for skewed alternatives.
• The application to the HIV dataset showcased the practical utility of the developed method.

Conclusions:

• Incorporating information about skewed alternative distributions significantly enhances power in multiple hypothesis testing.
• The proposed Bayesian rule provides a powerful and effective tool for directional hypothesis testing with skewed alternatives.
• This approach offers a valuable alternative to existing frequentist methods, particularly in fields with non-symmetric data patterns.