We consider a Bayesian method for simultaneous quantile regression on a realvariable. By monotone transformation, we can make both the response variableand the predictor variable take values in the unit interval. A representationof quantile function is given by a convex combination of two monotoneincreasing functions $\xi_1$ and $\xi_2$ not depending on the predictionvariables. In a Bayesian approach, a prior is put on quantile functions byputting prior distributions on $\xi_1$ and $\xi_2$. The monotonicity constrainton the curves $\xi_1$ and $\xi_2$ are obtained through a spline basis expansionwith coefficients increasing and lying in the unit interval. We put a Dirichletprior distribution on the spacings of the coefficient vector. A finite randomseries based on splines obeys the shape restrictions. We compare our approachwith a Bayesian method using Gaussian process prior through an extensivesimulation study and some other Bayesian approaches proposed in the literature.An application to a data on hurricane activities in the Atlantic region isgiven. We also apply our method on region-wise population data of USA for theperiod 1985--2010.
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