  Objective Bayesian inference procedures are derived for the parameters of the
multivariate random effects model generalized to elliptically contoured
distributions. The posterior for the overall mean vector and the between-study
covariance matrix is deduced by assigning two noninformative priors to the
model parameter, namely the Berger and Bernardo reference prior and the
Jeffreys prior, whose analytical expressions are obtained under weak
distributional assumptions. It is shown that the only condition needed for the
posterior to be proper is that the sample size is larger than the dimension of
the data-generating model, independently of the class of elliptically contoured
distributions used in the definition of the generalized multivariate random
effects model. The theoretical findings of the paper are applied to real data
consisting of ten studies about the effectiveness of hypertension treatment for
reducing blood pressure where the treatment effects on both the systolic blood
pressure and diastolic blood pressure are investigated.
