Minimax Predictive Priors

• Activity Number: 314
• Type: Topic Contributed
• Date/Time: Tuesday, August 9, 2005 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Feng Liang*+
• Companies: Duke University
• Keywords: Bayesian model selection ; minimax

Abstract

A key step in Bayesian model selection and averaging is prior specification. Due to the large amount of models involved (totally $2^p$ model if $p$ variables are considered), eliciting priors model by model is infeasible. So, it is of great interest to specify priors in an objective way. One of the difficulties here is that although we may use the same symbol to denote a ``common parameter'' across models, the parameter can change meanings across distinct models. It has been advocated to ``match priors'' across models to overcome this difficulty. If prediction is the goal, one should focus on the observables and regard models as convenient abstractions. So we suggest using the prior, which achieves (minimax) optimal prediction for the response variables, and then ``project'' them back on the model-specific parameters. In the context of linear regression model, it corresponds to mixture g-priors with Zellner-Siow prior as a special case. Properties such as consistency and extensions to nonparametric regression with constrained parameter space will be discussed as well.