Before revision:   The purpose of this paper is to compare the empirical Bayesian and approximation theoretic approaches to hierarchical learning, in terms of large data consistency, variance of estimators, robustness of the estimators to model misspecification, and computational cost.
After revision:  A crucial aspect of the success of this methodology, in a wide range of applications to complex and real-world problems, is hierarchical modeling and learning of hyperparameters. The purpose of this paper is to compare the empirical Bayesian and approximation theoretic approaches to hierarchical learning, in terms of large data consistency, variance of estimators, robustness of the estimators to model misspecification, and computational cost.