Bayesian Quantile Regression

Implementation of Bayesian Quantile Regression (BQR) with the use of Stan and R programming languages for a single predictor variable, i.e., y = b + wx + ε. In constrast to traditional Linear Regression which estimates the conditional mean function, i.e., E[y|x], BQR can be used to estimate any conditional quantile function of the form q_p(y|x), with p being the desired percentile. Bayesian inference is possible via the Asymmetric Laplace probability density function (see Yun & Moyeed, 2001). The BQR.stan script contains the Bayesian model and can be easily modified to accommodate multiple predictors, while the quantileRegression.R script fits a quantile regression with a numerical optimization alogirthm, as well as MCMC, for a simple data set provided in data-example.csv.

Edit: BQRv2.stan facilitates BQR with multiple predictors!

Reference

1. Yu, K. and Moyeed, R.A., 2001. Bayesian quantile regression. Statistics & Probability Letters, 54(4), pp.437-447.