In the era of big data, interval-valued data is quite common in real life and can be used to describe the uncertainty of variables. In this paper, we introduced random effects panel interval-valued data models based on the center and range method and constructed a Bayesian method for the models, including estimation and prediction. Some simulation studies indicate that the proposed Bayesian method performs well. Finally, our proposed panel interval-valued data Bayesian models were applied in forecasting of the Air Quality Index, and the experimental evaluation of actual data sets shows the advantages and the performance of our proposed models
