Bayesian Estimation of Prediction Error and Variable Selection in Linear Regression |
| |
Authors: | Andrew A. Neath Joseph E. Cavanaugh |
| |
Affiliation: | 1. Department of Mathematics and Statistics, Southern Illinois University Edwardsville, Edwardsville, IL 62025, USA E-mail: aneath@siue.edu;2. Department of Biostatistics, The University of Iowa, 200 Hawkins Drive, C22 GH, Iowa City, IA 52242, USA E-mail: joe-cavanaugh@uiowa.edu |
| |
Abstract: | An important statistical application is the problem of determining an appropriate set of input variables for modelling a response variable. In such an application, candidate models are characterized by which input variables are included in the mean structure. A reasonable approach to gauging the propriety of a candidate model is to define a discrepancy function through the prediction error associated with this model. An optimal set of input variables is then determined by searching for the candidate model that minimizes the prediction error. In this paper, we focus on a Bayesian approach to estimating a discrepancy function based on prediction error in linear regression. It is shown how this approach provides an informative method for quantifying model selection uncertainty. |
| |
Keywords: | Cp statistic discrepancy function model selection criterion |
|
|