Bayesian One-Sided Variable Selection.

Area of Science:

• Statistics
• Bayesian inference
• Regression analysis

Background:

• Traditional variable selection methods may not fully leverage prior knowledge about the direction of regression coefficients.
• Incorporating directional information can potentially improve the efficiency and accuracy of statistical models.

Purpose of the Study:

• To develop a novel Bayesian variable selection approach that explicitly accounts for the anticipated signs of regression coefficients.
• To enhance the selection of relevant variables and improve the identification of the best statistical model by utilizing directional priors.

Main Methods:

• Proposed a truncated g prior for specifying coefficient distributions with expected signs.
• Utilized multivariate one-sided tests and Bayesian model comparison based on posterior probabilities.
• Developed an adapted Bayesian model search for computational efficiency with numerous variables and a fully Bayesian approach for multiplicity correction.

Main Results:

• The proposed Bayesian one-sided variable selection procedure demonstrates a higher probability of including relevant variables when the anticipated direction is correct.
• Simulation studies and real data examples validate the method's performance.
• The adapted search method ensures fast computation for large-scale problems.

Conclusions:

• The novel Bayesian variable selection method effectively incorporates directional information, leading to improved model selection.
• The approach offers a statistically sound and computationally efficient tool for analyzing data with directional hypotheses.
• This method provides a valuable advancement in Bayesian variable selection techniques.