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Bayesian group selection in logistic regression with application to MRI data analysis.

Kyoungjae Lee¹, Xuan Cao²

¹Department of Statistics, Inha University, Incheon, South Korea.

|May 5, 2020

Summary

This study introduces a novel Bayesian logistic regression approach for high-dimensional data, achieving accurate group selection. The proposed hierarchical prior method demonstrates superior performance in simulations and real-world disease prediction tasks.

Keywords:

group spike and slab prior high-dimensional strong selection consistency

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Area of Science:

Statistics
Machine Learning
Biostatistics

Background:

High-dimensional data analysis often requires identifying significant covariate groups.
Bayesian methods offer advantages in uncertainty quantification for model selection.
Existing frequentist group selection methods lack theoretical Bayesian counterparts for logistic regression.

Purpose of the Study:

To develop and theoretically validate a Bayesian group selection method for logistic regression in high-dimensional settings.
To establish the first theoretical guarantees for Bayesian group selection consistency in this context.
To evaluate the proposed method's performance against existing state-of-the-art techniques.

Main Methods:

Implementation of a hierarchical group spike and slab prior for Bayesian logistic regression.
Theoretical analysis to establish strong group selection consistency of the posterior distribution.
Simulation studies across various scenarios to assess performance.
Application to a real-world magnetic resonance imaging dataset for Parkinson's disease prediction.

Main Results:

The proposed Bayesian method achieves strong group selection consistency under mild conditions.
Simulation results indicate superior performance compared to existing methods.
The method demonstrates practical utility in predicting Parkinson's disease from MRI data.

Conclusions:

The study provides the first theoretical foundation for Bayesian group selection consistency in high-dimensional logistic regression.
The developed method is effective and outperforms current approaches.
The approach shows promise for applications in medical imaging and disease prediction.