Prediction for Seemingly Unrelated Regressions

SUMMARY The seemingly unrelated regressions model is described and analysed from a Bayesian perspective. The predictive density for this model cannot, in general, be evaluated analytically. Two approximations are proposed and investigated. These are Gibbs sampling and a first-order approximation based on a Bayes estimate of the precision matrix. These approximations are then compared on simulated data and both appear to give good results. Extensions to allow for missing data are also discussed.