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Bayesian smoothing spline analysis of variance

Author

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  • Cheng, Chin-I.
  • Speckman, Paul L.

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.

Suggested Citation

  • Cheng, Chin-I. & Speckman, Paul L., 2012. "Bayesian smoothing spline analysis of variance," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 3945-3958.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:12:p:3945-3958
    DOI: 10.1016/j.csda.2012.05.020
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    References listed on IDEAS

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    1. Paul L. Speckman, 2003. "Fully Bayesian spline smoothing and intrinsic autoregressive priors," Biometrika, Biometrika Trust, vol. 90(2), pages 289-302, June.
    2. Liang, Feng & Paulo, Rui & Molina, German & Clyde, Merlise A. & Berger, Jim O., 2008. "Mixtures of g Priors for Bayesian Variable Selection," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 410-423, March.
    3. Sally Wood & Robert Kohn & Tom Shively & Wenxin Jiang, 2002. "Model selection in spline nonparametric regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(1), pages 119-139, January.
    4. Dongchu Sun & Paul Speckman, 2008. "Bayesian hierarchical linear mixed models for additive smoothing splines," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(3), pages 499-517, September.
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    Cited by:

    1. Tong, Xiaojun & He, Zhuoqiong Chong & Sun, Dongchu, 2018. "Estimating Chinese Treasury yield curves with Bayesian smoothing splines," Econometrics and Statistics, Elsevier, vol. 8(C), pages 94-124.

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