In this talk, we consider Bayesian variable selection in linear regression models with related predictors. We propose a generalized singular g-prior for the unknown parameters, which results in a closed-form expression of the marginal posterior distribution. A special prior on the model space is adopted to re?ect and maintain the hierarchical relationships among predictors. It is shown that the proposed approach is consistent in terms of model selection and prediction. Simulation studies and real data application are considered for illustrative purposes.

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