Inference with Normal-Jeffreys Prior Distributions in Quantile Regression

Decades after its discussion in (Koenker and Bassett, 1978), quantile regression (QR) has been the topic of great practical applications in many areas: economics, ecology, biology and so on.In this paper, we present Bayesian quantile regression using two level prior distributions.Specifically, we assume that the prior distribution of each regression coefficient is a zero mean normal prior distribution with unknown variance.Then, we assign noninformative Jeffreys prior distributions for the variances assuming they are independent.A Gibbs sampler algorithm is developed for the posterior inference.The new method is illustrated via simulations and a real dataset.