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.

As a typical form of symbolic data, interval-valued data provides an effective framework to analyze large-scale datasets. Most existing interval regression studies focus on classical methods, while research that incorporates heteroscedasticity within the Bayesian framework remains limited. This paper extends the existing parametric method for interval-valued data to a Bayesian heteroscedastic framework, and further develops the Bayesian Heteroscedastic Parametric Method (BHPM). By explicitly modeling heteroscedasticity in the regression structure, we conduct Bayesian inference using Gibbs sampling and the Metropolis–Hastings algorithm, thus enhancing the model's interpretability and generalization performance. Both simulation studies and real-data applications demonstrate that the extended BHPM achieves superior performance over traditional methods.