Model Selection and Multiple Testing - A Bayesian and Empirical Bayes Overview and some New Results

Understand

We provide a brief overview of both Bayes and classical model selection.

• We argue tentatively that model selection has at least two major goals, that of finding the correct model or predicting well, and that in general both these goals may not be achieved in an optimum manner by a single model selection rule.
• We discuss, briefly but critically, through a study of well-known model selection rules like AIC, BIC, DIC and Lasso, how these different goals are pursued in each paradigm.
• We introduce some new definitions of consistency, results and conjectures about consistency in high dimensional model selection problems.