Decoupling shrinkage and selection in Bayesian linear models: a posterior summary perspective

TL;DR

This paper reviews recent advances in Bayesian variable selection and shrinkage priors, proposing a posterior summary method that simplifies the full posterior distribution into a sequence of sparse predictors for linear models.

Contribution

It introduces a novel posterior summary approach that decouples shrinkage from variable selection, providing a clearer interpretation of Bayesian linear models.

Findings

Effective variable selection with sparse predictors

Improved interpretability of Bayesian models

Compatibility with various shrinkage priors

Abstract

Selecting a subset of variables for linear models remains an active area of research. This paper reviews many of the recent contributions to the Bayesian model selection and shrinkage prior literature. A posterior variable selection summary is proposed, which distills a full posterior distribution over regression coefficients into a sequence of sparse linear predictors.