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Table 1 Simulation results

From: Bayesian methods for expression-based integration of various types of genomics data

  σ 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
  1. Freq. EN means freqentist elastic net, which was run with mixing parameter (for penalty mixture) 0.5. The estimate of σ2 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.