A heteroscedastic parametric method with Bayesian inference for interval-valued regression 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.