Bayesian varying-coefficient models using adaptive regression splines

Varying-coefficient models provide a flexible framework for semiand 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 nonGaussian responses, where less alternatives are available. We illustrate the approach with a thorough application to two data sets analysed previously in the literature: the kyphosis data set with a binary response and survival data from the Veteran’s Administration lung cancer trial.