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.