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Bayesian Analysis for Penalized Spline Regression Using WinBUGS

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

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    Bibliographic Info

    Article provided by American Statistical Association in its journal Journal of Statistical Software.

    Volume (Year): 14 ()
    Issue (Month): i14 ()
    Pages:

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    Handle: RePEc:jss:jstsof:14:i14

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    Web page: http://www.jstatsoft.org/

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    1. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, October.
    2. Andrew Gelman, 2004. "Prior distributions for variance parameters in hierarchical models," Econometrics 0404001, EconWPA.
    3. Long Ngo & Matthew P. Wand, . "Smoothing with Mixed Model Software," Journal of Statistical Software, American Statistical Association, vol. 9(i01).
    4. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, October.
    5. 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.
    6. 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.
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    Cited by:
    1. Márcio Laurini, 2012. "Dynamic Functional Data Analysis with Nonparametric State Space Models," IBMEC RJ Economics Discussion Papers 2012-01, Economics Research Group, IBMEC Business School - Rio de Janeiro.
    2. Bellio, Ruggero & Grassetti, Luca, 2011. "Semiparametric stochastic frontier models for clustered data," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 71-83, January.
    3. Choudhary, Pankaj K., 2007. "Semiparametric regression for assessing agreement using tolerance bands," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6229-6241, August.
    4. Botts, Carsten H. & Daniels, Michael J., 2008. "A flexible approach to Bayesian multiple curve fitting," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5100-5120, August.
    5. Laurini, Fabrizio & Pauli, Francesco, 2009. "Smoothing sample extremes: The mixed model approach," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3842-3854, September.
    6. 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.
    7. Welham, S.J. & Thompson, R., 2009. "A note on bimodality in the log-likelihood function for penalized spline mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 920-931, February.

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