# Bayesian Quantile Regression Using Random B-spline Series Prior

arXiv: https://arxiv.org/abs/1609.02950 · HTML: https://mlsanity.com/paper/1609.02950/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Sep 2016.

## Built on by (most cited first, 2 of 2)

- [Projected Statistical Methods for Distributional Data on the Real Line with the Wasserstein Metric](https://mlsanity.com/paper/2101.09039/) (2021)
- [A Two-step Metropolis Hastings Method for Bayesian Empirical Likelihood Computation with Application to Quantile Regression and Bayesian Model Selection](https://mlsanity.com/paper/2209.01269/) (2022)

## Abstract (arXiv)

We consider a Bayesian method for simultaneous quantile regression on a real variable. By monotone transformation, we can make both the response variable and the predictor variable take values in the unit interval. A representation of quantile function is given by a convex combination of two monotone increasing functions xi1 and xi2 not depending on the prediction variables. In a Bayesian approach, a prior is put on quantile functions by putting prior distributions on xi1 and xi2. The monotonicity constraint on the curves xi1 and xi2 are obtained through a spline basis expansion with coefficients increasing and lying in the unit interval. We put a Dirichlet prior distribution on the spacings of the coefficient vector. A finite random series based on splines obeys the shape restrictions. We compare our approach 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. We also apply our method on region-wise population data of USA for the period 1985--2010.