Estimating the smoothing parameter in generalized spline-based regression

SummarySmoothing with splines requires a smoothing parameter which is most often obtained by cross-validation. Interpreting splines from a Bayesian point of view this is an empirical Bayesian approach. A fully Bayesian approach with a (hyper-) prior for the smoothing parameter is computationally more demanding even for Gaussian data and really accessible only using simulation methods. Smoothing in generalized regression models is presented in a Bayesian interpretation and tried with Gaussian and binary data using the implementation of Gibbs sampling in BUGS. The results are compared to those obtained by cross-validation. The approach essentially does work but convergence of just the smoothing parameter turns out to be crucial. The sensitivity of the estimated function values w.r.t. to the prior is satisfactory.