  A two-stage approach is proposed to overcome the problem in quantile
regression, where separately fitted curves for several quantiles may cross. The
standard Bayesian quantile regression model is applied in the first stage,
followed by a Gaussian process regression adjustment, which monotonizes the
quantile function whilst borrowing strength from nearby quantiles. The two
stage approach is computationally efficient, and more general than existing
techniques. The method is shown to be competitive with alternative approaches
via its performance in simulated examples.
