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，我们针对函数型标量回归模型（FOSR）中的变量选择问题，提出了一种新的贝叶斯方法。该方法通过引入潜变量实现自适应选择，能够自主确定应纳入函数型标量回归模型的变量数量及具体变量。仿真实验展示了该方法的优越特性，包括系数估计的准确性和变量选择的高效性。此外，我们将该方法与BGLSS方法、group LASSO、group MCP及group SCAD等主流方法进行了对比研究。基于巴西新冠肺炎确诊病例数据集及社会经济数据的实证分析表明，本文提出的贝叶斯变量选择模型具有极强竞争力，展现出显著的预测精度与选择效能。