A bayesian analysis for estimating the common mean of independent normal populations using the gibbs sampler

Combining information from several independent normal populations to estimate a common parameter has applications in meta-analysis and is an important statistical problem. For this application a Bayesian technique via the Gibbs sampler is adopted. Given several normal independent populations with a common mean and different variances, it is possible to perform a complete Bayesian analysis that determines the posterior distribution of the important parameter, the common mean, by using the Gibbs sampler. The methodology is illustrated using two examples. Characteristics such as the mean and the 95% Credible Region are presented. In example 2 a hypotheses test is performed.