Bayesian Elastic Network Models:Full Gibbs Sampling Algorithms

As mixing the least absolute and the least square techniques,the elastic net mod-els have represented the flexibility and good performance in variable selection,estimation,and prediction,especially when the number of predictors is large and/or there are high correlations among the predictors.However,as the full conditional posterior of the regularization coefficients is a distribution with in-tractable normalizing constant,the ordinary Metropolis-Hastings algorithm can not sample directly from it,which leads to that a full Bayesian method is unavail-able by far for analyzing the elastic models.The existing Bayesian approaches,where a Monte Carlo expectation maximization(MCEM)algorithm is used to update the regularization coefficients instead of sampling,are semi-Bayesian in essence.We propose an exchange algorithm to generate sample from the full con-ditional posterior of the regularization coefficients,and consequently develop a full Bayesian sampling-based method to analyze the elastic models.Simulations verify the feasibility and effectiveness,and results show that the proposed method perform better than the existing methods.We apply the proposed method to a real data example.