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Fully Bayesian spline smoothing and intrinsic autoregressive priors

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  • Paul L. Speckman

Abstract

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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    Citations

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    Cited by:

    1. 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.
    2. 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.
    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. 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.
    5. Robert T. Krafty & Ori Rosen & David S. Stoffer & Daniel J. Buysse & Martica H. Hall, 2017. "Conditional Spectral Analysis of Replicated Multiple Time Series With Application to Nocturnal Physiology," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1405-1416, October.
    6. Theodore Eisenberg & Thomas Eisenberg & Martin T. Wells & Min Zhang, 2015. "Addressing the Zeros Problem: Regression Models for Outcomes with a Large Proportion of Zeros, with an Application to Trial Outcomes," Journal of Empirical Legal Studies, John Wiley & Sons, vol. 12(1), pages 161-186, March.
    7. 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.
    8. Cheng, Chin-I. & Speckman, Paul L., 2012. "Bayesian smoothing spline analysis of variance," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 3945-3958.
    9. 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.
    10. Krivobokova, Tatyana & Serra, Paulo & Rosales, Francisco & Klockmann, Karolina, 2022. "Joint non-parametric estimation of mean and auto-covariances for Gaussian processes," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    11. Peter F. Craigmile & Peter Guttorp, 2022. "Rejoinder to the discussion on “A combined estimate of global temperature”," Environmetrics, John Wiley & Sons, Ltd., vol. 33(3), May.

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