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Spatially Adaptive Bayesian P-Splines with Heteroscedastic Errors

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Author Info

  • Ciprian Crainiceanu

    (Johns Hokins Bloomberg School of Public Health, Department of Biostatistics)

  • David Ruppert

    (School of Operational Research & Industrial Engineering, Cornell University)

  • Raymond Carroll

    (Department of Statistics, Texas A&M University)

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    Abstract

    An increasingly popular tool for nonparametric smoothing are penalized splines (P-splines) which use low-rank spline bases to make computations tractable while maintaining accuracy as good as smoothing splines. This paper extends penalized spline methodology by both modeling the variance function nonparametrically and using a spatially adaptive smoothing parameter. These extensions have been studied before, but never together and never in the multivariate case. This combination is needed for satisfactory inference and can be implemented effectively by Bayesian \mbox{MCMC}. The variance process controlling the spatially-adaptive shrinkage of the mean and the variance of the heteroscedastic error process are modeled as log-penalized splines. We discuss the choice of priors and extensions of the methodology,in particular, to multivariate smoothing using low-rank thin plate splines. A fully Bayesian approach provides the joint posterior distribution of all parameters, in particular, of the error standard deviation and penalty functions. In the multivariate case we produce maps of the standard deviation and penalty functions. Our methodology can be implemented using the Bayesian software WinBUGS.

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    File URL: http://www.bepress.com/cgi/viewcontent.cgi?article=1061&context=jhubiostat
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    Bibliographic Info

    Paper provided by Berkeley Electronic Press in its series Johns Hopkins University Dept. of Biostatistics Working Paper Series with number 1061.

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    Date of creation: 27 Sep 2004
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    Handle: RePEc:bep:jhubio:1061

    Note: oai:bepress.com:jhubiostat-1061
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    Related research

    Keywords: Knot selection; MCMC; Mixed models; Multivariate smoothing; Spatially adaptive penalty; Thin-plate splines;

    References

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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. Andrew Gelman, 2004. "Prior distributions for variance parameters in hierarchical models," Econometrics 0404001, EconWPA.
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    Cited by:
    1. Blöchl, Andreas, 2014. "Trend Estimation with Penalized Splines as Mixed Models for Series with Structural Breaks," Discussion Papers in Economics 18446, University of Munich, Department of Economics.
    2. Leitenstorfer, Florian & Tutz, Gerhard, 2007. "Knot selection by boosting techniques," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4605-4621, May.

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