Prior Knowledge Guided Ultra-high Dimensional Variable Screening with Application to Neuroimaging Data

Area of Science:

• Statistics
• Bayesian Inference
• High-Dimensional Data Analysis

Background:

• Variable screening is crucial for dimension reduction in ultrahigh dimensional settings.
• Existing methods often fail to leverage valuable prior knowledge specific to applications.
• Bayesian modeling offers a flexible framework for incorporating prior information.

Purpose of the Study:

• To develop a unified Bayesian variable screening procedure for linear regression models.
• To incorporate diverse types of prior knowledge into the screening process.
• To establish theoretical properties and demonstrate practical advantages of the proposed method.

Main Methods:

• Developed posterior mean screening (PMS) statistics tailored for different prior knowledge types.
• Established the screening consistency property for PMS under various prior specifications.
• Analyzed the robustness of PMS to prior misspecifications and its performance relative to HOLP.

Main Results:

• PMS demonstrates screening consistency across different prior knowledge scenarios.
• The method is robust to inaccuracies in prior information.
• Correctly specified prior knowledge significantly enhances selection accuracy compared to HOLP and other methods.

Conclusions:

• The proposed Bayesian variable screening (PMS) offers a unified and flexible approach for dimension reduction.
• Incorporating application-specific prior knowledge via PMS substantially improves screening performance.
• The method shows promise for analyzing complex datasets, as demonstrated in neuroimaging data analysis.