Bayesian Estimation of a Meta-analysis model using Gibbs sampler

A hierarchical Bayesian model is investigated. This model can accommodate study heterogeneity in meta-analyses. The joint posterior distribution is derived by multiplying the likelihood and priors on this model. The conditional posterior distribution of all parameters is obtained for Gibbs sampler algorithm. A simulation study is then performed to demonstrate the validity of the Gibbs sampler in terms of parameter estimation.