Bayesian smoothing spline analysis of variance

Chin I. Cheng, Paul L. Speckman

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Smoothing spline ANOVA (SSANOVA) provides an approach to semiparametric function estimation based on an ANOVA type of decomposition. Wahba et al. (1995) decomposed the regression function based on a tensor sum decomposition of inner product spaces into orthogonal subspaces, so the effects of the estimated functions from each subspace can be viewed independently. Recent research related to smoothing spline ANOVA focuses on either frequentist approaches or a Bayesian framework for variable selection and prediction. In our approach, we seek "objective" priors especially suited to estimation. The prior for linear terms including level effects is a variant of the Zellner-Siow prior (Zellner and Siow, 1980), and the prior for a smooth effect is specified in terms of effective degrees of freedom. We study this fully Bayesian SSANOVA model for Gaussian response variables, and the method is illustrated with a real data set.

Original languageEnglish
Pages (from-to)3945-3958
Number of pages14
JournalComputational Statistics and Data Analysis
Volume56
Issue number12
DOIs
StatePublished - Dec 2012

Keywords

  • Bayesian
  • Reproducing kernel
  • Smoothing spline ANOVA
  • Zellner-Siow prior

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