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 coefficients determining
the shape of the spline. Since the spline can be represented as
design matrix times unknown (basis) coefficients, it is
straightforward to include additionally a vector of covariates with
fixed effects, 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.