  In this paper, we propose a new horseshoe-type prior hierarchy for adaptively
shrinking spline-based functional effects towards a predefined vector space of
parametric functions. Instead of shrinking each spline coefficient towards
zero, we use an adapted horseshoe prior to control the deviation from the
predefined vector space. For this purpose, the modified horseshoe prior is set
up with one scale parameter per spline and not one per coefficient. The
presented prior allows for a large number of basis functions to capture all
kinds of functional effects while the estimated functional effect is prevented
from a highly oscillating overfit. We achieve this by integrating a smoothing
penalty similar to the random walk prior commonly applied in Bayesian P-spline
priors. In a simulation study, we demonstrate the properties of the new prior
specification and compare it to other approaches from the literature.
Furthermore, we showcase the applicability of the proposed method by estimating
the energy consumption in Germany over the course of a day. For inference, we
rely on Markov chain Monte Carlo simulations combining Gibbs sampling for the
spline coefficients with slice sampling for all scale parameters in the model.
