Model Selection Principles in Misspecified Models

Understand

Model selection is of fundamental importance to high dimensional modeling featured in many contemporary applications.

• Classical principles of model selection include the Kullback-Leibler divergence principle and the Bayesian principle, which lead to the Akaike information criterion and Bayesian information criterion when models are correctly specified.
• Yet model misspecification is unavoidable when we have no knowledge of the true model or when we have the correct family of distributions but miss some true predictor.
• In this paper, we propose a family of semi-Bayesian principles for model selection in misspecified models, which combine the strengths of the two well-known principles.