Penalized complexity priors for degrees of freedom in Bayesian P-splines. (December 2016)

• Record Type: Journal Article
• Authors: Ventrucci, Massimo; Rue, Håvard
• Is Part Of: Statistical modelling. Volume 16:Number 6(2016)
• Page Start: 429
• Page End: 453
• Publication Date: 2016-12
• Subjects: Bayesian P-splines -- degrees of freedom -- penalized complexity priors -- penalized spline regression; Linear models (Statistics) -- Periodicals; Mathematical models -- Periodicals; Modèles linéaires (Statistique) -- Périodiques; Modèles mathématiques -- Périodiques; Modèle statistique; Modèle linéaire; Modélisation statistique; Périodique électronique (Descripteur de forme); Ressource Internet (Descripteur de forme); 519.5011
• DOI: 10.1177/1471082X16659154
• Languages: English
• ISSNs: 1471-082X

Abstract

Abstract: Bayesian penalized splines (P-splines) assume an intrinsic Gaussian Markov random field prior on the spline coefficients, conditional on a precision hyper-parameterτ . Prior elicitation ofτ 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.