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.

翻译：本文在假设数据服从椭圆等高分布的条件下，当模型参数被赋予Berger-Bernardo参照先验与Jeffreys先验时，提出了多变量随机效应模型参数的贝叶斯推断流程。我们开发了一种基于混合吉布斯采样的新数值算法，用于从后验分布中抽取样本。通过广泛的模拟研究，将该新方法与文献中先前推导的两种Metropolis-Hastings算法进行了比较。研究结果在实际中应用于十项关于高血压治疗对降低血压有效性的研究，其中同时考察了治疗对收缩压和舒张压的影响。