Considering the field of functional data analysis, we developed a new Bayesian method for variable selection in function-on-scalar regression (FOSR). Our approach uses latent variables, allowing an adaptive selection since it can determine the number of variables and which ones should be selected for a function-on-scalar regression model. 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 comparative studies with the main competing methods, such as the BGLSS method as well as the group LASSO, the group MCP and the group SCAD. We also used a COVID-19 dataset and some socioeconomic data from Brazil for real data application. In short, the proposed Bayesian variable selection model is extremely competitive, showing significant predictive and selective quality.

翻译：在函数型数据分析领域，我们提出了一种新的贝叶斯方法，用于函数-on-标量回归（FOSR）中的变量选择。该方法通过引入潜变量实现自适应选择，能够自动确定函数-on-标量回归模型中应选变量数量及其具体变量。模拟研究展示了所提方法的主要特性，包括系数估计的准确性以及变量选择的高效性。此外，我们与主流竞争方法（如BGLSS方法、群组LASSO、群组MCP及群组SCAD）进行了比较研究，并利用巴西COVID-19数据集及社会经济数据进行了实际应用验证。总的来说，所提出的贝叶斯变量选择模型具有极强竞争力，表现出显著的预测能力与选择质量。