Intrinsic priors for model comparison in multivariate normal regression

In Moreno et al. (Rev R Acad Cien Ser A Mat 97:53-61, 2003) an objective Bayesian model comparison procedure for univariate normal regression models based on intrinsic priors was provided. However, in many applications the regression models entertained are multidimensional, and hence an extension of the procedure to this setting is required. This technical paper provides the intrinsic priors and their Bayes factors for testing multidimensional normal regression models. The sampling distributions of the sufficient statistic for model comparison are also found when sampling from both the null and the alternative models. This is a key tool for proving consistency of the model selection procedure based on the Bayes factor for intrinsic priors.