标题： 高维回归中的分组方差分解的R2先验 显示英文标题

标题： R2 priors for Grouped Variance Decomposition in High-dimensional Regression

摘要： 我们引入了Group-R2分解先验，这是一种分层收缩先验，将基于R2的先验扩展到具有已知预测变量组的结构化回归设置。 通过在两个阶段对决定系数R2的先验分布进行分解，首先是跨组，然后是组内，该先验使得对模型复杂性和稀疏性的可解释控制成为可能。 我们推导了该先验的理论性质，包括系数的边缘分布、尾部行为以及与有效模型复杂性的联系。 通过模拟研究，我们评估了在哪些条件下分组相比不考虑分组的先验能提高预测性能和参数恢复效果。 我们的结果为先验设定提供了实用指导，并突显了将分组纳入基于R2的收缩先验的优势和局限性。 显示英文摘要

摘要： We introduce the Group-R2 decomposition prior, a hierarchical shrinkage prior that extends R2-based priors to structured regression settings with known groups of predictors. By decomposing the prior distribution of the coefficient of determination R2 in two stages, first across groups, then within groups, the prior enables interpretable control over model complexity and sparsity. We derive theoretical properties of the prior, including marginal distributions of coefficients, tail behavior, and connections to effective model complexity. Through simulation studies, we evaluate the conditions under which grouping improves predictive performance and parameter recovery compared to priors that do not account for groups. Our results provide practical guidance for prior specification and highlight both the strengths and limitations of incorporating grouping into R2-based shrinkage priors.