Bayesian quantile regression model with linear inequality constraints

• Published in: Statistics and computing Vol. 35; no. 4
• Main Authors: Yu, Jialei, Dai, Jun, Xu, Min, Ullah, Sami
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Nature B.V 01.08.2025
• Subjects: Bayesian analysis; Confined spaces; Constraints; Crop yield; Generalized inverse; Inverse Gaussian probability distribution; Linear functions; Parameter estimation; Quantiles; Regression models; Sampling methods
• ISSN: 0960-3174; 1573-1375
• DOI: 10.1007/s11222-025-10646-2

Linear inequality constraints enhance the precision of parameter estimation by constraining parameters to a more confined space. This paper introduces a Bayesian quantile regression model with linear inequality constraints. To rigorously enforce these inequality constraints within the Bayesian framework, we adopt truncated prior distributions. Leveraging asymmetric Laplace distributions, we propose two novel Gibbs sampling methods based on truncated normal and truncated Laplace prior distributions, which involve sampling from truncated normal and generalized inverse Gaussian distributions, respectively. Our approach extends the constraints from solely inequality-based to a comprehensive framework incorporating both equality and inequality constraints. Simulation studies demonstrate that the proposed method outperforms traditional quantile regression without constraints across various error distributions. Furthermore, we apply this method to analyze non-performing loan ratios and corn yield data, showcasing its practical applicability.