Abstract
IMS Collections 2008, Vol. 3, 267-281 Rescaled spike and slab models are a new Bayesian variable selection method
for linear regression models. In high dimensional orthogonal settings such
models have been shown to possess optimal model selection properties. We review
background theory and discuss applications of rescaled spike and slab models to
prediction problems involving orthogonal polynomials. We first consider global
smoothing and discuss potential weaknesses. Some of these deficiencies are
remedied by using local regression. The local regression approach relies on an
intimate connection between local weighted regression and weighted generalized
ridge regression. An important implication is that one can trace the effective
degrees of freedom of a curve as a way to visualize and classify curvature.
Several motivating examples are presented.