Statistical Modelling 1 (2001), 195–211

Bayesian Varying-coefficient Models using Adaptive Regression Splines

Clemens Biller and Ludwig Fahrmeir
Ludwig Maximilians University Munich, Germany
Department of Statistics
Ludwig Maximilians University Munich
Ludwigstr. 33, D–80539 Munich, Germany


Varying-coefficient models provide a flexible framework for semi-and nonparametric generalized regression analysis. We present a fully Bayesian B-spline basis function approach with adaptive knot selection. For each of the unknown regression functions or varying coefficients, the number and location of knots and the B-spline coefficients are estimated simultaneously using reversible jump Markov chain Monte Carlo sampling. The overall procedure can therefore be viewed as a kind of Bayesian model averaging. Although Gaussian responses are covered by the general framework, the method is particularly useful for fundamentally non-Gaussian responses, where less alternatives are available. We illustrate the approach with a thorough application to two data sets analyzed previously in the literature: the kyphosis data set with a binary response and survival data from the Veteran's Administration lung cancer trial.


B-spline basis; Knot selection; Non-Gaussian response; Non- and semiparametric regression; Reversible jump Markov chain Monte Carlo.


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