Accounting for Model Uncertainty in Seemingly Unrelated Regressions

This article considers inference in a Bayesian seemingly unrelated regression (SUR) model where the set of regressors is assumed unknown a priori. That is, we allow for uncertainty in the covariate set by defining a prior distribution on the model space. The posterior inference is analytically intractable and we adopt computer-intensive simulation using variable dimension Markov chain Monte Carlo algorithms to approximate quantities of interest. Applications are given for vector autoregression (VAR) models of unknown order and multivariate spline models with unknown knot points.