A simple new approach to variable selection in regression, with application to genetic fine mapping

Area of Science:

• Statistics
• Genetics
• Computational Biology

Background:

• Variable selection is crucial in linear regression for identifying relevant predictors.
• Quantifying uncertainty in variable selection remains a challenge, especially with highly correlated variables.
• Existing methods may struggle with sparse effects and high dimensionality common in genetic data.

Purpose of the Study:

• Introduce a novel approach for variable selection in linear regression.
• Develop a method that quantifies uncertainty in variable selection.
• Address limitations of current methods in settings with correlated variables and sparse effects.

Main Methods:

• Propose the Sum of Single Effects (SuSiE) model, representing coefficients as sums of single-effect vectors.
• Introduce Iterative Bayesian Stepwise Selection (IBSS), a Bayesian analogue of stepwise selection.
• Utilize variational approximation to optimize posterior distribution and derive uncertainty summaries.

Main Results:

• IBSS provides a distribution on variables, capturing selection uncertainty.
• The SuSiE-IBSS approach generates Credible Sets for variable selection.
• Demonstrated superior performance over existing methods in numerical experiments, particularly for genetic fine-mapping.

Conclusions:

• The SuSiE-IBSS method offers a robust and computationally efficient approach to variable selection.
• The approach effectively quantifies uncertainty, providing valuable insights for complex datasets.
• Applicable to genetic fine-mapping and potentially broader variable selection problems.