Bayesian Inference for Linear Models Subject to Linear Inequality Constraints

The normal linear model, with sign or other linear inequality constraints on its coefficients, arises very commonly in many scientific applications. Given inequality constraints Bayesian inference is much simpler than classical inference, but standard Bayesian computational methods become impractical when the posterior probability of the inequality constraints (under a diffuse prior) is small. This paper shows how the Gibbs sampling algorithm can provide an alternative, attractive approach to inference subject to linear inequality constraints in this situation, and how the GHK probability simulator may be used to assess the posterior probability of the constraints. The editor and a referee, who bear no responsibility for any errors or omissions, have provided suggestions that improved the paper. This work was supported in part by National Science Foundation Grant SES-9210070. The views expressed in this paper are those of the author and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System.