  In this paper, we present the Bayesian inference procedures for the
parameters of the multivariate random effects model derived under the
assumption of an elliptically contoured distribution when the Berger and
Bernardo reference and the Jeffreys priors are assigned to the model
parameters. We develop a new numerical algorithm for drawing samples from the
posterior distribution, which is based on the hybrid Gibbs sampler. The new
approach is compared to the two Metropolis-Hastings algorithms, which were
previously derived in the literature, via an extensive simulation study. The
results are implemented in practice by considering 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.
