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

Massimo Ventrucci*, Håvard Rue

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


Bayesian penalized splines (P-splines) assume an intrinsic Gaussian Markov random field prior on the spline coefficients, conditional on a precision hyper-parameter τ. Prior elicitation of τ 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.

Original languageEnglish (US)
Pages (from-to)429-453
Number of pages25
JournalStatistical Modelling
Issue number6
StatePublished - Dec 1 2016
Externally publishedYes


  • Bayesian P-splines
  • degrees of freedom
  • penalized complexity priors
  • penalized spline regression

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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