2024/12/19 by Eric Yanchenko, Yanchenko, Eric, Kaoru Irie +3 · 1 citation
Economics, Econometrics and Finance · #FOS: Computer and information sciences #Methodology (stat.ME) #Spatial and Panel Data Analysis
paper · pdf · doi:10.48550/arxiv.2412.15293
openalex publication_date 2024/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Shrinkage priors are a popular Bayesian paradigm to handle sparsity in high-dimensional regression. Still limited, however, is a flexible class of shrinkage priors to handle grouped sparsity, where covariates exhibit some natural grouping structure. This paper proposes a novel extension of the R2-induced Dirichlet Decomposition (R2D2) prior to accommodate grouped variable selection in linear regression models. The proposed method, called the Group R2D2 prior, employs a Dirichlet prior distribution on the coefficient of determination for each group, allowing for a flexible and adaptive shrinkage that operates at both group and individual variable levels. This approach improves the original R2D2 prior to handle grouped predictors, providing a balance between within-group dependence and group-level sparsity. We present several theoretical properties of this proposed prior distribution while also developing a Markov Chain Monte Carlo algorithm. Through simulation studies and real-data analysis, we demonstrate that our method outperforms traditional shrinkage priors in terms of both estimation accuracy, inference and prediction.