A semiparametric quantile Bayesian method for interval-valued data models

As the capability to handle massive datasets with interval-valued data becomes increasingly prominent, some scholars have conducted in-depth research on interval-valued regression models. However, few works are devoted to exploring Bayesian methods for interval-valued data. In this paper, a semiparametric quantile Bayesian method for interval-valued data models is proposed. We extend the center and range method and the Min-Max method for interval-valued semiparametric quantile regression models to the Bayesian framework. In this study, we develop an MCMC sampling algorithm to generate posterior samples and further obtain Bayesian estimates and predictive results based on the nonparametric part estimated by B-splines. The experimental results of synthetic and real datasets show that, compared with classical models, the proposed Bayesian model has superior forecasting performances.