Adaptive shrinkage of smooth functional effects towards a predefined functional subspace

TL;DR

This paper introduces a novel Bayesian prior for spline-based functional effects that adaptively shrinks towards a predefined subspace, balancing flexibility and overfitting prevention.

Contribution

The paper develops a new horseshoe-type prior with one scale parameter per spline, enabling adaptive shrinkage towards a predefined functional space.

Findings

The prior effectively prevents overfitting in spline models.

Simulation studies demonstrate the prior's desirable properties.

Application to energy data shows practical utility.

Abstract

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.