Bayesian Model Averaging for Linear Regression Models

We consider the problem of accounting for model uncertainty in linear regression models. Conditioning on a single selected model ignores model uncertainty, and thus leads to the underestimation of uncertainty when making inferences about quantities of interest. A Bayesian solution to this problem involves averaging over all possible models (i.e., combinations of predictors) when making inferences about quantities of Adrian E. Raftery is Professor of Statistics and Sociology, David Madigan is Assistant Professor of Statistics, both at the Department of Statistics,University of Washington, Box 354322, Seattle, WA 98195-4322. Jennifer Hoeting is Assistant Professor of Statistics at the Department of Statistics, Colorado State University, Fort Collins, CO 80523. The research of Raftery and Hoeting was partially supported by ONR Contract N-00014-91-J-1074. Madigan's research was partially supported by NSF grant no. DMS 92111627. The authors are grateful to Danika Lew for research assistance and the Editor, the Associate Editor, two anonymous referees and David Draper for very helpful comments that greatly improved the article.