Sorted $\ell_1$ Penalized Estimation (SLOPE) models, that perform either variable or group selection, control the false discovery rate (FDR) under orthogonal settings with known noise, but such settings are rare in practice. Under general conditions, cross-validation is the default model selection approach for SLOPE, yet it targets predictive performance rather than FDR control. We address this gap for the SLOPE family of models by proposing new Bayesian approaches, Bayesian Group SLOPE (BGSLOPE) and Bayesian Sparse-group SLOPE (BSGS). BGSLOPE and BSGS embed group-based SLOPE models into a spike-and-slab framework, with BSGS providing a continuous spike-and-slab framework for sparse-group models. We further introduce Two-step Orthogonal (TSO), which transforms a general setting into an orthogonal one to recover SLOPE's FDR control properties. Through extensive synthetic and real data studies comparing all major model selection strategies for SLOPE models, the proposed Bayesian models consistently control FDR, achieve higher power, and outperform competing methods in prediction.

翻译：排序ℓ1惩罚估计（SLOPE）模型可执行变量选择或分组选择，并在已知噪声的正交设定下控制错误发现率（FDR），但此类设定在实践中较为罕见。在一般条件下，交叉验证是SLOPE模型的默认模型选择方法，但其目标在于预测性能而非FDR控制。针对SLOPE模型家族的这一不足，我们提出新的贝叶斯方法——贝叶斯分组SLOPE（BGSLOPE）与贝叶斯稀疏分组SLOPE（BSGS）。BGSLOPE与BSGS将基于分组的SLOPE模型嵌入spike-and-slab框架，其中BSGS为稀疏分组模型提供连续spike-and-slab框架。我们进一步提出两步正交化方法（TSO），该方法将一般设定转化为正交设定以恢复SLOPE的FDR控制特性。通过综合合成数据与真实数据对SLOPE模型所有主要模型选择策略的对比研究，所提出的贝叶斯模型能够稳定控制FDR，获得更高统计功效，并在预测性能上优于其他竞争方法。