Bayesian quantile regression using random B-spline series prior

A Bayesian method for simultaneous quantile regression on a real variable is considered. By monotone transformation, the response variable and the predictor variable are transformed into the unit interval. A representation of quantile function is given by a convex combination of two monotone increasing functions ξ1 and ξ2 not depending on the prediction variables. In a Bayesian approach, a prior is put on quantile functions by putting prior distributions on ξ1 and ξ2. The monotonicity constraint on the curves ξ1 and ξ2 are obtained through a spline basis expansion with coefficients increasing and lying in the unit interval. A Dirichlet prior distribution is put on the spacings of the coefficient vector. A finite random series based on splines obeys the shape restrictions. The proposed method is extended to multidimensional predictors such that the quantile regression depends on the predictors through an unknown linear combination only. In the simulation study, the proposed approach is compared with a Bayesian method using Gaussian process prior through an extensive simulation study and some other Bayesian approaches proposed in the literature. An application to a data on hurricane activities in the Atlantic region is given. The proposed method is also applied on region-wise population data of USA for the period 1985–2010.