
$\hat{{\mathit{\sigma}}^{\mathbf{2}}}$

95% CI

90% CI

MSE ratio

MSE ratio


 
coverage

coverage

(train data)

(test data)


Our method

0.9073

0.9778

0.8889

0.2827

9.4630

Maximum likelihood

0.1181

1.00

0.9667

1

1

Bayesian lasso

0.6407

0.9667

0.9111

0.3727

8.858

Freq. lasso (1 SE)

1.2020

NA

NA

0.0983

8.1163

Freq. lasso (min)

0.6379

NA

NA

0.1851

8.8374

Freq. EN (1 SE)

0.9278

NA

NA

0.1273

8.4439

Freq. EN (min)

0.7012

NA

NA

0.1684

8.7154

 Freq. EN means freqentist elastic net, which was run with mixing parameter (for penalty mixture) 0.5. The estimate of σ^{2} is the posterior mean for our method and the Bayesian lasso. For the others, it is the mean sum of squared error. ‘CI’ is credible interval for Bayesian methods and confidence interval for frequentist methods. Note that for the frequentist lasso and elastic net, it is not possible to obtain standard errors for the coefficients set to 0, and therefore, we cannot construct the CI’s. The penalty choice of ‘1 SE’ means we used the largest parameter with error within one standard error of the minimum error, while ‘min’ means we used the parameter with minimum error (from cross validation). MSE ratio is the mean squared error from least squares divided by the MSE from the respective method. NA indicates not applicable.