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Bayesian Analysis for Penalized Spline Regression Using WinBUGS

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  • Crainiceanu, Ciprian M.
  • Ruppert, David
  • Wand, Matthew P.

Abstract

Penalized splines can be viewed as BLUPs in a mixed model framework, which allows the use of mixed model software for smoothing. Thus, software originally developed for Bayesian analysis of mixed models can be used for penalized spline regression. Bayesian inference for nonparametric models enjoys the flexibility of nonparametric models and the exact inference provided by the Bayesian inferential machinery. This paper provides a simple, yet comprehensive, set of programs for the implementation of nonparametric Bayesian analysis in WinBUGS. Good mixing properties of the MCMC chains are obtained by using low-rank thin-plate splines, while simulation times per iteration are reduced employing WinBUGS specific computational tricks.

Suggested Citation

  • Crainiceanu, Ciprian M. & Ruppert, David & Wand, Matthew P., 2005. "Bayesian Analysis for Penalized Spline Regression Using WinBUGS," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 14(i14).
  • Handle: RePEc:jss:jstsof:v:014:i14
    DOI: http://hdl.handle.net/10.18637/jss.v014.i14
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    References listed on IDEAS

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    1. Andrew Gelman, 2004. "Prior distributions for variance parameters in hierarchical models," EERI Research Paper Series EERI_RP_2004_06, Economics and Econometrics Research Institute (EERI), Brussels.
    2. Ngo, Long & Wand, Matthew P., 2004. "Smoothing with Mixed Model Software," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 9(i01).
    3. Berry S. M. & Carroll R. J & Ruppert D., 2002. "Bayesian Smoothing and Regression Splines for Measurement Error Problems," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 160-169, March.
    4. Andrew Gelman, 2004. "Prior distributions for variance parameters in hierarchical models," Econometrics 0404001, University Library of Munich, Germany.
    5. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, October.
    6. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, October.
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    Blog mentions

    As found by EconAcademics.org, the blog aggregator for Economics research:
    1. Method of the month: Semiparametric models with penalised splines
      by Sam Watson in The Academic Health Economists' Blog on 2017-12-19 13:00:05

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    14. Gosoniu, L. & Vounatsou, P. & Sogoba, N. & Maire, N. & Smith, T., 2009. "Mapping malaria risk in West Africa using a Bayesian nonparametric non-stationary model," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3358-3371, July.
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