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Fully Bayesian spline smoothing and intrinsic autoregressive priors


  • Paul L. Speckman


There is a well-known Bayesian interpretation for function estimation by spline smoothing using a limit of proper normal priors. The limiting prior and the conditional and intrinsic autoregressive priors popular for spatial modelling have a common form, which we call partially informative normal. We derive necessary and sufficient conditions for the propriety of the posterior for this class of partially informative normal priors with noninformative priors on the variance components, a condition crucial for successful implementation of the Gibbs sampler. The results apply for fully Bayesian smoothing splines, thin-plate splines and L-splines, as well as models using intrinsic autoregressive priors. Copyright Biometrika Trust 2003, Oxford University Press.

Suggested Citation

  • Paul L. Speckman, 2003. "Fully Bayesian spline smoothing and intrinsic autoregressive priors," Biometrika, Biometrika Trust, vol. 90(2), pages 289-302, June.
  • Handle: RePEc:oup:biomet:v:90:y:2003:i:2:p:289-302

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    Cited by:

    1. Jing Cao & Chong Z. He & Kimberly M. Suedkamp Wells & Joshua J. Millspaugh & Mark R. Ryan, 2009. "Modeling Age and Nest-Specific Survival Using a Hierarchical Bayesian Approach," Biometrics, The International Biometric Society, vol. 65(4), pages 1052-1062, December.
    2. Jing Cao & S. Stokes, 2008. "Bayesian IRT Guessing Models for Partial Guessing Behaviors," Psychometrika, Springer;The Psychometric Society, vol. 73(2), pages 209-230, June.
    3. Yu Yue & Paul Speckman & Dongchu Sun, 2012. "Priors for Bayesian adaptive spline smoothing," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(3), pages 577-613, June.
    4. Takemi Yanagimoto & Toshio Ohnishi, 2014. "Permissible boundary prior function as a virtually proper prior density," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(4), pages 789-809, August.
    5. repec:eee:csdana:v:56:y:2012:i:12:p:3945-3958 is not listed on IDEAS
    6. 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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