Objective Bayesian Model Selection in Generalised Additive Models with Penalised Splines

We propose an objective Bayesian approach to the selection of covariates and their penalised splines transformations in generalised additive models. The methodology is based on a combination of continuous mixtures of <i>g</i>-priors for model parameters and a multiplicity-correction prior for the models themselves. We introduce our approach in the normal model and extend it to non-normal exponential families. A simulation study and an application with binary outcome is provided. An efficient implementation is available in the R-package “hypergsplines”.