  We consider the estimation of generalized additive models using basis
expansions coupled with Bayesian model selection. Although Bayesian model
selection is an intuitively appealing tool for regression splines, its use has
traditionally been limited to Gaussian additive regression because of the
availability of a tractable form of the marginal model likelihood. We extend
the method to encompass the exponential family of distributions using the
Laplace approximation to the likelihood. Although the approach exhibits success
with any Gaussian-type prior distribution, there remains a lack of consensus
regarding the best prior distribution for nonparametric regression through
model selection. We observe that the classical unit information prior
distribution for variable selection may not be well-suited for nonparametric
regression using basis expansions. Instead, our investigation reveals that
mixtures of g-priors are more suitable. We consider various mixtures of
g-priors to evaluate the performance in estimating generalized additive models.
Furthermore, we conduct a comparative analysis of several priors for knots to
identify the most practically effective strategy. Our extensive simulation
studies demonstrate the superiority of model selection-based approaches over
other Bayesian methods.
