In this work, we developed a new Bayesian method for variable selection in function-on-scalar regression (FOSR). Our method uses a hierarchical Bayesian structure and latent variables to enable an adaptive covariate selection process for FOSR. Extensive simulation studies show the proposed method's main properties, such as its accuracy in estimating the coefficients and high capacity to select variables correctly. Furthermore, we conducted a substantial comparative analysis with the main competing methods, the BGLSS (Bayesian Group Lasso with Spike and Slab prior) method, the group LASSO (Least Absolute Shrinkage and Selection Operator), the group MCP (Minimax Concave Penalty), and the group SCAD (Smoothly Clipped Absolute Deviation). Our results demonstrate that the proposed methodology is superior in correctly selecting covariates compared with the existing competing methods while maintaining a satisfactory level of goodness of fit. In contrast, the competing methods could not balance selection accuracy with goodness of fit. We also considered a COVID-19 dataset and some socioeconomic data from Brazil as an application and obtained satisfactory results. In short, the proposed Bayesian variable selection model is highly competitive, showing significant predictive and selective quality.

翻译：本文提出了一种新的贝叶斯方法，用于标量响应函数回归（FOSR）中的变量选择。该方法利用分层贝叶斯结构和潜变量，实现了FOSR中协变量的自适应选择过程。广泛模拟研究展示了所提方法的主要特性，例如系数估计的准确性以及正确选择变量的高能力。此外，我们与主要竞争方法——BGLSS（基于尖峰-板先验的贝叶斯组套索）方法、组LASSO（最小绝对收缩与选择算子）、组MCP（极小极大凹惩罚）和组SCAD（平滑剪裁绝对偏差）——进行了实质性比较分析。结果表明，在保持良好拟合优度的同时，所提方法在正确选择协变量方面优于现有竞争方法。相比之下，竞争方法无法平衡选择准确性与拟合优度。我们还考虑了巴西的COVID-19数据集及部分社会经济数据作为应用案例，获得了令人满意的结果。简而言之，所提贝叶斯变量选择模型具有高度竞争力，展现出显著的预测和选择性能。