Bayesian Bridge Estimation:an Exact Gibbs Sampler Algorithm

The bridge estimate for high-dimensional linear regression has many interesting properties,such as oracle,sparsity and unbiasedness.However,in the existing Bayesian regularization methods that is based on normal scale mixing priors,the conditional posterior density of the concave parameter,which controls the shape of penalty function,not only is a nonstandard density,but also contains an intractable factor.The resultant MCMC algorithm was inexact and time consuming as the value of the intractable factor should be calculated frequently via numerical approximation method.This paper proposes sampling the concave parameter from its full conditional posterior via the exchange algorithm to obtain an exact method of analysis.The feasibility and effectiveness of the proposed method are verified by simulation,and the results show that the proposed method is better than the existing methods.The proposed method is also applied to real data analysis.