Bayesian Estimation of Linear Statistical Model Bias

The linear statistical model provides a flexible approach to quantifying the relationship between a set of real-valued input variables and a real-valued response. A scientifically relevant goal is to determine which input variables have only a minor effect, or no effect, on the response. We show how this decision can be framed as an estimation problem by defining a bias parameter for the linear statistical model. A Bayesian approach to estimating the model bias leads us to an easily interpreted quantification of the uncertainty inherent in a statistical decision. AMS Subject Classification: 62C10, 62F15, 62J05