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In this paper, we present the Bayesian inference procedures for theparameters of the multivariate random effects model derived under theassumption of an elliptically contoured distribution when the Berger andBernardo reference and the Jeffreys priors are assigned to the modelparameters. We develop a new numerical algorithm for drawing samples from theposterior distribution, which is based on the hybrid Gibbs sampler. The newapproach is compared to the two Metropolis-Hastings algorithms, which werepreviously derived in the literature, via an extensive simulation study. Theresults are implemented in practice by considering ten studies about theeffectiveness of hypertension treatment for reducing blood pressure where thetreatment effects on both the systolic blood pressure and diastolic bloodpressure are investigated.

Gibbs sampler approach for objective Bayeisan inference in elliptical multivariate random effects model