Bayesian estimation of the linear regression model with an uncertain interval constraint on coefficients

This article considers Bayesian inference in the interval constrained normal linear regression model. Whereas much of the previous literature has concentrated on the case where the prior constraint is correctly specified, our framework explicitly allows for the possibility of an invalid constraint. We adopt a non-informative prior and uncertainty concerning the interval restriction is represented by two prior odds ratios. The sampling theoretic risk of the resulting Bayesian interval pre-test estimator is derived, illustrated and explored.