Bayesian Geoadditive Seemingly Unrelated Regression

Parametric seemingly unrelated regression (SUR) models are a common
tool for multivariate regression analysis when error variables are
reasonably correlated, so that separate univariate analysis may
result in inefficient estimates of covariate effects. A weakness of
parametric models is that they require strong assumptions on the
functional form of possibly nonlinear effects of metrical
covariates. In this paper, we develop a Bayesian semiparametric SUR
model, where the usual linear predictors are replaced by more
flexible additive predictors allowing for simultaneous
nonparametric estimation of such covariate effects and of spatial
effects. The approach is based on appropriate smoothness priors
which allow different forms and degrees of smoothness in a general
framework. Inference is fully Bayesian and uses recent Markov chain
Monte Carlo techniques.