Bayesian estimation approach for linear regression models with linear inequality restrictions

This paper presents a Bayesian inference approach for univariate and multivariate linear models where the regression coefficients are subject to known linear combinations restricted by known intervals. Unlike most previous Bayesian studies on the univariate case—which assume that the constraint matrix defining the set of linear inequalities is a full-rank square matrix—our proposed method imposes no such condition. We develop a Bayesian estimation procedure for regression parameters in both univariate and multivariate settings that accommodate arbitrary constraint matrices. The efficiency of our method is evaluated through simulation studies, and its practical utility is illustrated by analyzing two real datasets.