Spatially adaptive Bayesian penalized splines with heteroscedastic errors

Ciprian M. Crainiceanu, David Ruppert, Raymond J. Carroll, Adarsh Joshi, Billy Goodner

Research output: Contribution to journalArticlepeer-review

63 Scopus citations


Penalized splines have become an increasingly popular tool for nonparametric smoothing because of their use of low-rank spline bases, which makes computations tractable while maintaining accuracy as good as smoothing splines. This article extends penalized spline methodology by both modeling the variance function nonparametrically and using a spatially adaptive smoothing parameter. This combination is needed for satisfactory inference and can be implemented effectively by Bayesian MCMC. The variance process controlling the spatially adaptive shrinkage of the mean and the variance of the heteroscedastic error process are modeled as log-penalized splines. We discuss the choice of priors and extensions of the methodology, in particular, to multi-variate smoothing. A fully Bayesian approach provides the joint posterior distribution of all parameters, in particular, of the error standard deviation and penalty functions. MATLAB, C, and FORTRAN programs implementing our methodology are publicly available.

Original languageEnglish (US)
Pages (from-to)265-288
Number of pages24
JournalJournal of Computational and Graphical Statistics
Issue number2
StatePublished - Jun 2007


  • Heteroscedasticity
  • MCMC
  • Multivariate smoothing
  • Regression splines
  • Spatially adaptive penalty
  • Thin-plate splines
  • Variance functions

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Discrete Mathematics and Combinatorics


Dive into the research topics of 'Spatially adaptive Bayesian penalized splines with heteroscedastic errors'. Together they form a unique fingerprint.

Cite this