Shared kernel Bayesian screening.

Area of Science:

• Statistics
• Bioinformatics
• Computational Biology

Background:

• Accurate testing for distributional equality between groups is crucial in various scientific fields.
• Existing methods often struggle with high-dimensional data and shared distributional features among variables.
• Screening variables with common support, modes, and skewness patterns presents analytical challenges.

Purpose of the Study:

• To propose a novel Bayesian testing method for assessing equality of distribution between groups.
• To enhance the performance of variable screening by incorporating shared distributional features.
• To develop a scalable framework for high-dimensional data analysis.

Main Methods:

• Utilized a Bayesian approach with kernel mixtures to model distributions.
• Incorporated shared kernels and a common probability of group differences to borrow information across variables and groups.
• Employed a finite mixture model with Dirichlet priors for efficient high-dimensional data handling.

Main Results:

• Developed a simple and scalable testing framework suitable for high-dimensional data.
• Derived closed asymptotic forms for the posterior probability of equivalence in two-group comparisons.
• Demonstrated consistency of the method even under model misspecification.

Conclusions:

• The proposed Bayesian kernel mixture method offers improved performance for testing distributional equality.
• The framework effectively handles high-dimensional data by leveraging shared information across variables and groups.
• The method shows promise, as evidenced by its favorable comparison to existing techniques on DNA methylation array data from a breast cancer study.