Bayesian analysis of the linear regression constraints by Gibbs sampler

Abstract<br /> In this paper we consider parameter estimation in a linear regression setting with inequality linear constraints on the regression parameters. Most other research on this topic has typically been addressed from a Bayesian perspective. In this paper we apply Bayesian approach with Gibbs sampler to generate samples from the posterior distribution. However, these implementations can often exhibit poor mixing and slow convergence. This paper overcomes these limitations with a new implementation of the Gibbs sampler. In addition, this procedure allows for the number of constraints to exceed the parameter dimension and is able to cope with equality linear constraints.