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We propose an objective Bayesian approach to the selection of covariates andtheir penalised splines transformations in generalised additive models.Specification of a reasonable default prior for the model parameters andcombination with a multiplicity-correction prior for the models themselves iscrucial for this task. Here we use well-studied and well-behaved continuousmixtures of g-priors as default priors. We introduce the methodology in thenormal model and extend it to non-normal exponential families. A simulationstudy and an application from the literature illustrate the proposed approach.An efficient implementation is available in the R-package "hypergsplines".

Mixtures of g-Priors for Generalised Additive Model Selection with Penalised Splines