Adaptive Bayesian Regression Splines in Semiparametric Generalized Linear Models

This paper presents a fully Bayesian approach to regression splines with automatic knot selection in generalized semiparametric models for fundamentally non Gaussian responses In a basis function representation of the regression spline we use a B spline basis The reversible jump Markov chain Monte Carlo method allows for simultaneous estimation both of the number of knots and the knot placement together with the unknown basis coe cients determining the shape of the spline Since the spline can be represented as design matrix times unknown basis coe cients it is straightforward to include additionally a vector of covariates with xed e ects yielding a semiparametric model The method is illustrated with data sets from the literature for curve estimation in generalized linear models the Tokyo rainfall data and the coal mining disaster data and by a credit scoring problem for generalized semiparametric models