  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.
