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

Ruiqin Tian; Ke Liu; Guangyu Wang; Dengke Xu; Ruiqin Tian; Ke Liu; Guangyu Wang; Dengke Xu

doi:10.3934/era.2026207

Electronic Research Archive

2026, Volume 34, Issue 7: 4698-4724. doi: 10.3934/era.2026207

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Research article

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

1.
School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China
2.
School of Economics, Hangzhou Dianzi University, Hangzhou 310018, China

Received: 07 April 2026 Revised: 10 May 2026 Accepted: 18 May 2026 Published: 01 June 2026

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.
- interval-valued data,
- Bayesian regression,
- heteroscedasticity,
- parametrized method
Citation: Ruiqin Tian, Ke Liu, Guangyu Wang, Dengke Xu. A heteroscedastic parametric method with Bayesian inference for interval-valued regression models[J]. Electronic Research Archive, 2026, 34(7): 4698-4724. doi: 10.3934/era.2026207

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Abstract

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.

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