Penalized complexity priors for degrees of freedom in Bayesian P-splines

TL;DR

This paper introduces Penalized Complexity priors for degrees of freedom in Bayesian P-splines, providing an interpretable way to specify priors on model complexity, with practical implementation for Gaussian data.

Contribution

It develops a novel class of PC priors for degrees of freedom in Bayesian P-splines, enhancing prior elicitation and interpretability.

Findings

PC priors effectively control model complexity

Implementation details for Gaussian data are provided

Improved prior elicitation for Bayesian P-splines

Abstract

Bayesian P-splines assume an intrinsic Gaussian Markov random field prior on the spline coefficients, conditional on a precision hyper-parameter $\tau$. Prior elicitation of $\tau$ is difficult. To overcome this issue we aim to building priors on an interpretable property of the model, indicating the complexity of the smooth function to be estimated. Following this idea, we propose Penalized Complexity (PC) priors for the number of effective degrees of freedom. We present the general ideas behind the construction of these new PC priors, describe their properties and show how to implement them in P-splines for Gaussian data.