Bayesian P-Splines

TLDR: In this article, a Bayesian version of P-spline is proposed for modeling nonlinear smooth effects of covariates within the additive and varying coefficient models framework, which is particularly useful in situations with changing curvature of the underlying smooth function or with highly oscillating functions.

Abstract: P-splines are an attractive approach for modeling nonlinear smooth effects of covariates within the additive and varying coefficient models framework. In this article, we first develop a Bayesian version for P-splines and generalize in a second step the approach in various ways. First, the assumption of constant smoothing parameters can be replaced by allowing the smoothing parameters to be locally adaptive. This is particularly useful in situations with changing curvature of the underlying smooth function or with highly oscillating functions. In a second extension, one-dimensional P-splines are generalized to two-dimensional surface fitting for modeling interactions between metrical covariates. In a last step, the approach is extended to situations with spatially correlated responses allowing the estimation of geoadditive models. Inference is fully Bayesian and uses recent MCMC techniques for drawing random samples from the posterior. In a couple of simulation studies the performance of Bayesian P-spline...