Bayesian P-Splines

P-splines are an attractive approach for modelling nonlinear smooth
effects of covariates within the generalized additive and varying
coefficient models framework. In this paper we propose a Bayesian
version for P-splines and generalize the approach for one
dimensional curves to two dimensional surface fitting for modelling
interactions between metrical covariates. A Bayesian approach to
P-splines has the advantage of allowing for simultaneous estimation
of smooth functions and smoothing parameters. Moreover, it can
easily be extended to more complex formulations, for example to
mixed models with random effects for serially or spatially
correlated response. Additionally, 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 where the function is highly oscillating. 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-splines is studied and compared to other
approaches in the literature. We illustrate the approach by a
complex application on rents for flats in Munich.