Abstract
Bayesian penalized splines (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.