Robust Bayesian model selection

• Main Authors: LI, Yong, YU, Jun
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2013
• Subjects: Model selection; Model misspecification; Artificial posterior distribution; Sandwich-covariance matrix; Markov chain Monte Carlo; Econometrics
• Online Access: https://ink.library.smu.edu.sg/soe_research/2112; https://ink.library.smu.edu.sg/context/soe_research/article/3112/viewcontent/Robust_Bayesian_model_selection_2013.pdf
• Institution: Singapore Management University

This paper extends the robust Bayesian inference in misspecified models of Müller (2013, Econometrica) to Bayesian model selection of a set of misspecified models. It is shown that when a model is misspecified, under the Kullback-Leibler loss function, the risk associated with Müller's posterior is less (weakly) than that with the original posterior distribution asymptotically. Based on this new result, two new information criteria are proposed for model selection under model misspecification. Sufficient conditions are provided for the risk associated with Müller's posterior to be strictly smaller.