2 8 M ay 2 00 8 Adaptive Ridge Selector ( ARiS ) May 28 , 2008

We introduce a new shrinkage variable selection operator for linear models which we term the adaptive ridge selector (ARiS). This approach is inspired by the relevance vector machine (RVM), which uses a Bayesian hierarchical linear setup to do variable selection and model estimation. Extending the RVM algorithm, we include a proper prior distribution for the precisions of the regression coefficients, v j ∼ f(v −1 j |η), where η is a scalar hyperparameter. A novel fitting approach which utilizes the full set of posterior conditional distributions is applied to maximize the joint posterior distribution p(β, σ2,v−1|y, η) given the value of the hyper-parameter η. An empirical Bayes method is proposed for choosing η. This approach is contrasted with other regularized least squares