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，用于函数型标量回归（FOSR）中的变量选择。该方法通过引入潜变量实现自适应选择，能够自动确定函数型标量回归模型中应纳入的变量数量及其具体选择。模拟研究表明，所提方法在系数估计精度和变量正确选择能力方面表现出良好特性。此外，我们与BGLSS方法、分组LASSO、分组MCP及分组SCAD等主要竞争方法进行了对比研究。在真实数据应用中，我们还采用了巴西的COVID-19数据集及部分社会经济数据。总体而言，所提出的贝叶斯变量选择模型具有极强的竞争力，展现了显著的预测性能与选择能力。