Selecting Linear Models Under the Bayesian Paradigm with Focus on Good Prediction Over a User-Specified Distribution on the Covariate Space

• Activity Number: 470
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Adam Lee Pintar*+ and Christine Anderson-Cook and Huaiqing Wu
• Companies: National Institute of Standards and Technology and Los Alamos National Laboratory and Iowa State University
• Keywords: Model Selection ; Deviance Information Criterion ; Posterior Probability ; Bayesian Model Averaging ; Correlated Variables

Abstract

Model selection is an important part of building linear regression models in the Bayesian paradigm. If unimportant explanatory variables are included, posterior distributions will have inflated variance. If important explanatory variable are excluded, posterior distributions can miss their (unknown) target. Several model selection methodologies currently exist. For instance, one could choose the model with the smallest deviance information criterion, the model with the largest posterior probability, or the model whose terms all have posterior probability greater than 0.5. A common theme to all of these methodologies is that they consider only the observed data. We propose a model selection methodology that focuses on good prediction over a user-specified distribution on the covariate space. The methodology quantifies the prediction ability of all models under consideration at many covariate points sampled from the user-specified distribution. Then, a best model is identified by graphically comparing the distributions of prediction abilities. The methodology is illustrated via an example, and a simulation study highlighting its potential is presented.