Method Posterior Distributions of Latent Parameters Bayesian lasso Bayesian ridge Bayesian adaptive lasso Bayesian elastic net Bayesian group lasso* (K Groups) *For Bayesian Group Lasso the shrinkage prior distribution is with corresponding mixing density and posterior distribution , where , , , , , , is a diagonal matrix with diagonal elements , is a diagonal matrix with diagonal elements is a diagonal matrix with diagonal elements . IG refers to inverse Gaussian distribution.

Table 2: Scale mixture representation of different shrinkage priors and corresponding posterior distributions.