Bayesian Inference Quantile Regression

Classical quantile regression is an important regression method and model for the inference of conditional quantiles of a response variable given a vector of covariates. It can be used to measure the effect of covariates not only in the center of a distribution, but also in the tails. Bayesian methods involve formal combination through the use of Bayes’s theorem of a prior distribution or belief about the value of a quantity of interest (for example, experience and expert opinion) based on evidence not derived from the study under analysis and a summary of the information available from the data collected in the study (or likelihood) to produce an updated or posterior distribution of the quantity of interest. Bayesian inference quantile regression has emerged in recent years. A brief review and discussion of the methods will be made, including Bayesian parametric quantile regression, Bayesian nonparametric quantile regression, Bayesian spatial quantile regression, Bayesian censored quantile regression, prior selection, variable selection and some applications and comparison examples.