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

arXiv: https://arxiv.org/abs/1408.0464 · HTML: https://mlsanity.com/paper/1408.0464/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Aug 2014.

## Built on by (most cited first, 8 of 8)

- [Bayesian subset selection and variable importance for interpretable prediction and classification](https://mlsanity.com/paper/2104.10150/) (2021)
- [Subset selection for linear mixed models](https://mlsanity.com/paper/2107.12890/) (2021)
- [Inference on covariance structure in high-dimensional multi-view data](https://mlsanity.com/paper/2509.02772/) (2025)
- [Decoupling Shrinkage and Selection for the Bayesian Quantile Regression](https://mlsanity.com/paper/2107.08498/) (2021)
- [Bayesian adaptive and interpretable functional regression for exposure profiles](https://mlsanity.com/paper/2203.00784/) (2022)
- [Factorized Fusion Shrinkage for Dynamic Relational Data](https://mlsanity.com/paper/2210.00091/) (2022)
- [Heterogeneous Treatment Effect Estimation under Noncompliance in the Illinois Workplace Wellness Study with Bayesian Tree Ensembles](https://mlsanity.com/paper/2408.07765/) (2024)
- [Variational Bayesian Bow tie Neural Networks with Shrinkage](https://mlsanity.com/paper/2411.11132/) (2024)

## Abstract (arXiv)

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.