Bayesian analysis for a constrained linear multiple regression problem for predicting the new crop of apples

In this article, a Bayesian model for a constrained linear regression problem is studied. The constraints arise naturally in the context of predicting the new crop of apples for the year ahead. We utilize the Gibbs sampler to obtain solutions to integration problems associated with Bayesian analysis. The Bayesian methodology with the Gibbs sampler is shown to be particularly suited to the constrained problem. Further, alternative methods such as ordinary and inequality-constrained least square estimations are investigated; and comparisons among Bayesian, ordinary, and inequality-constrained least square estimations are also made.