The Bayesian Elastic Net

Elastic net (1) is a flexible regularization and variable selection method which can handle the data with more predictors than the sampler size. This paper proposes a Bayesian elastic net method to solve the elastic net model using the Gibbs sampler. While it yields theoretically equivalent estimators, the Bayesian elastic net method has two major advantages over the frequentist elastic net method. Firstly, as a Bayesian method, the distributional results on the estimates are straightforward, making the statistical inference available. Secondly, it chooses the two penalty parameter simultaneously, avoiding the “double shrinkage problem ” in the elastic net method. Real data examples and simulation studies shows that two methods behave comparably but the Bayesian elastic net makes much less false exclusion of the predictors