The paper introduces a variable selection method called the rescaled spike and slab model, which combines frequentist and Bayesian approaches. The authors study the importance of hierarchical prior specifications and their connections to frequentist generalized ridge regression estimation. They focus on continuous bimodal priors for hypervariance parameters and the effect of scaling on the posterior mean through penalization. Several model selection strategies are developed and analyzed theoretically. The paper demonstrates the importance of selective shrinkage for effective variable selection in terms of risk misclassification and shows how to verify a procedure's ability to reduce model uncertainty using a specialized forward selection strategy. The rescaled spike and slab model is shown to be effective in reducing model uncertainty. The main findings include: 1. The use of a spike and slab model with a continuous bimodal prior for hypervariances has distinct advantages in calibration, but its effect diminishes as the sample size increases. 2. Rescaling the data by a $\sqrt{n}$ factor and introducing a variance inflation parameter $\lambda_n$ allows the prior to have a nonvanishing effect, achieving sample size universality. 3. $\lambda_n$ controls the amount of shrinkage in the posterior mean relative to ordinary least squares (OLS), and if $\lambda_n \to \infty$ and $\lambda_n / n \to 0$, the posterior mean asymptotically converges to OLS. 4. For model selection, the most interesting case is when $\lambda_n = n$, which achieves an oracle risk misclassification performance relative to OLS under a correctly chosen hypervariance. 5. The posterior mean, combined with a reliable thresholding rule, is shown to be a highly effective Bayesian test statistic, outperforming traditional OLS model selection procedures. 6. A forward stepwise selection strategy is introduced to verify the ability of a model averaging procedure to reduce model uncertainty. The paper also discusses the selective shrinkage property of the posterior mean, which is crucial for effective variable selection.The paper introduces a variable selection method called the rescaled spike and slab model, which combines frequentist and Bayesian approaches. The authors study the importance of hierarchical prior specifications and their connections to frequentist generalized ridge regression estimation. They focus on continuous bimodal priors for hypervariance parameters and the effect of scaling on the posterior mean through penalization. Several model selection strategies are developed and analyzed theoretically. The paper demonstrates the importance of selective shrinkage for effective variable selection in terms of risk misclassification and shows how to verify a procedure's ability to reduce model uncertainty using a specialized forward selection strategy. The rescaled spike and slab model is shown to be effective in reducing model uncertainty. The main findings include: 1. The use of a spike and slab model with a continuous bimodal prior for hypervariances has distinct advantages in calibration, but its effect diminishes as the sample size increases. 2. Rescaling the data by a $\sqrt{n}$ factor and introducing a variance inflation parameter $\lambda_n$ allows the prior to have a nonvanishing effect, achieving sample size universality. 3. $\lambda_n$ controls the amount of shrinkage in the posterior mean relative to ordinary least squares (OLS), and if $\lambda_n \to \infty$ and $\lambda_n / n \to 0$, the posterior mean asymptotically converges to OLS. 4. For model selection, the most interesting case is when $\lambda_n = n$, which achieves an oracle risk misclassification performance relative to OLS under a correctly chosen hypervariance. 5. The posterior mean, combined with a reliable thresholding rule, is shown to be a highly effective Bayesian test statistic, outperforming traditional OLS model selection procedures. 6. A forward stepwise selection strategy is introduced to verify the ability of a model averaging procedure to reduce model uncertainty. The paper also discusses the selective shrinkage property of the posterior mean, which is crucial for effective variable selection.