Model averaging for sparse seemingly unrelated regression using Bayesian networks among the errors

Abstract Multivariate Bayesian linear regression (MBLR) is a popular statistical tool with many applications in variety of scientific fields. However, shortcoming potential model over-complexity, as the assumes that all responses depend on same covariates and errors are mutually pairwise correlated. The class seemingly unrelated (SUR) models generalizes MBLR by allowing for response-specific covariate sets. In recent work it has been proposed to employ Gaussian graphical learning sparse SUR (SSUR) conditional independencies among errors. SSUR infers undirected edges errors, Reversible Jump Markov Chain Monte Carlo (RJMCMC) inference algorithm relies approximations marginal likelihoods. this paper, we propose new refined replaces graphs (Gaussian models) directed acyclic networks). Unlike earlier model, our therefore able learn some And derive RJMCMC does not require particular, present an sampling covariance matrices coherent given graph. allows exact averaging across both: sets graphs.