Bayesian nonparametric quantile regression using splines

A new technique based on Bayesian quantile regression that models the dependence of a quantile of one variable on the values of another using a natural cubic spline is presented. Inference is based on the posterior density of the spline and an associated smoothing parameter and is performed by means of a Markov chain Monte Carlo algorithm. Examples of the application of the new technique to two real environmental data sets and to simulated data for which polynomial modelling is inappropriate are given. An aid for making a good choice of proposal density in the Metropolis–Hastings algorithm is discussed. The new nonparametric methodology provides more flexible modelling than the currently used Bayesian parametric quantile regression approach.