  Accurately selecting and estimating smooth functional effects in additive
models with potentially many functions is a challenging task. We introduce a
novel Demmler-Reinsch basis expansion to model the functional effects that
allows us to orthogonally decompose an effect into its linear and nonlinear
parts. We show that our representation allows to consistently estimate both
parts as opposed to commonly employed mixed model representations. Equipping
the reparameterized regression coefficients with normal beta prime spike and
slab priors allows us to determine whether a continuous covariate has a linear,
a nonlinear or no effect at all. We provide new theoretical results for the
prior and a compelling explanation for its superior Markov chain Monte Carlo
mixing performance compared to the spike-and-slab group lasso. We establish an
efficient posterior estimation scheme and illustrate our approach along effect
selection on the hazard rate of a time-to-event response in the geoadditive Cox
regression model in simulations and data on survival with leukemia.
