  Quantile regression has received increased attention in the statistics
community in recent years. This article adapts an auxiliary variable method,
commonly used in Bayesian variable selection for mean regression models, to the
fitting of quantile regression curves. We focus on the fitting of regression
splines, with unknown number and location of knots. We provide an efficient
algorithm with Metropolis-Hastings updates whose tuning is fully automated. The
method is tested on simulated and real examples and its extension to additive
models is described. Finally we propose a simple postprocessing procedure to
deal with the problem of the crossing of multiple separately estimated quantile
curves.
