Statistical Modelling 8 (2008), 141168
Simultaneous probability statements for Bayesian P-splines
Andreas Brezger
Hypovereinsbank München
Germany
Stefan Lang
Department of Statistics,
University of Innsbruck,
Universitätsstr. 15,
A6020 Innsbruck
Austria
eMail:
stefan.lang@uibk.ac.at
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.
Keywords:
Bayesian p-values; generalized additive models; MCMC; model choice
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