Regularization in regression: comparing Bayesian and frequentist methods in a poorly informative situation

We propose a global noninformative approach for Bayesian variable selection that builds on Zellner's g-priors and is similar to Liang et al. (2008). Our proposal does not require any kind of calibration. In the case of a benchmark, we compare Bayesian and frequentist regularization approaches under a low informative constraint when the number of variables is almost equal to the number of observations. The simulated and real dataset experiments we present here highlight the appeal of Bayesian regularization methods, when compared with alternatives. They dominate frequentist methods in the sense they provide smaller prediction errors while selecting the most relevant variables in a parsimonious way.