Bayesian partially-protected regularization as a model selection tool

Yasir Atalan, Selim Yaman and Jeff Gill

Journal of Applied Statistics, 2026, vol. 53, issue 7, 1316-1341

Abstract: This work first describes Bayesian Partially-Protected Lasso (BPL), which combines the power of Bayesian Lasso with the ability to protect key theoretical explanatory variables from shrinkage to a zero effect in the model. This approach allows researchers to identify protected and non-protected variables so that data with many explanatory variables can be efficiently machine-explored without sacrificing theoretically important predictors. We provide the statistical background, algorithms, examples, and easy to use tools in an R package. We then introduce BPEN – Bayesian Protected Elastic Net estimation process that builds on the idea of the Bayesian Partially-Protected Lasso. Since the Elastic Net adds a second penalty term to the standard Lasso it provides a more flexible regularization process. This is a novel approach that combines the robustness of the Elastic Net in sifting through potentially large sets of variables while simultaneously safeguarding the integrity of those grounded in theoretical principles.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:taf:japsta:v:53:y:2026:i:7:p:1316-1341

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DOI: 10.1080/02664763.2025.2559025

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