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Simultaneous probability statements for Bayesian P-splines

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  • Andreas Brezger

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  • Stefan Lang

    ()

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    Abstract

    P-splines are a popular approach for fitting nonlinear effects of continuous covariates in semiparametric regression models. Recently, a Bayesian version for P-splines has been developed on the basis of Markov chain Monte Carlo simulation techniques for inference. In this work we adopt and generalize the concept of Bayesian contour probabilities to additive models with Gaussian or multicategorical responses. More specifically, we aim at computing the maximum credible level (sometimes called Bayesian p-value) for which a particular parameter vector of interest lies within the corresponding highest posterior density (HPD) region. We are particularly interested in parameter vectors that correspond to a constant, linear or more generally a polynomial fit. As an alternative to HPD regions simultaneous credible intervals could be used to define pseudo contour probabilities. Efficient algorithms for computing contour and pseudo contour probabilities are developed. The performance of the approach is assessed through simulation studies. Two applications on the determinants of undernutrition in developing countries and the health status of trees show how contour probabilities may be used in practice to assist the analyst in the model building process.

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    File URL: http://eeecon.uibk.ac.at/wopec2/repec/inn/wpaper/2007-08.pdf
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    Bibliographic Info

    Paper provided by Faculty of Economics and Statistics, University of Innsbruck in its series Working Papers with number 2007-08.

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    Length: 29
    Date of creation: May 2007
    Date of revision:
    Handle: RePEc:inn:wpaper:2007-08

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    Web page: http://www.uibk.ac.at/fakultaeten/volkswirtschaft_und_statistik/index.html.en
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    Keywords: Bayesian p-values; contour probabilities; generalized additive models; Rao-Blackwell estimator;

    This paper has been announced in the following NEP Reports:

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    1. John Maindonald, . "Generalized Additive Models: An Introduction with R," Journal of Statistical Software, American Statistical Association, vol. 16(b03).
    2. Ludwig Fahrmeir & Stefan Lang, 2001. "Bayesian Semiparametric Regression Analysis of Multicategorical Time-Space Data," Annals of the Institute of Statistical Mathematics, Springer, vol. 53(1), pages 11-30, March.
    3. Andreas Brezger & Thomas Kneib & Stefan Lang, . "BayesX: Analyzing Bayesian Structural Additive Regression Models," Journal of Statistical Software, American Statistical Association, vol. 14(i11).
    4. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika van der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639.
    5. Chib S. & Jeliazkov I., 2001. "Marginal Likelihood From the Metropolis-Hastings Output," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 270-281, March.
    6. Marx, Brian D. & Eilers, Paul H. C., 1998. "Direct generalized additive modeling with penalized likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 28(2), pages 193-209, August.
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