Hyper-g priors for generalised additive model selection

We propose an automatic Bayesian approach to the selection of covariates and penalised splines transformations thereof in generalised additive models. Specification of a hyper-g prior for the model parameters and a multiplicity-correction prior for the models themselves is crucial for this task. We introduce the methodology in the normal model and illustrate it with an application to diabetes data. Extension to non-normal exponential families is finally discussed