Bayes Estimation of a Common Mean of Several Normal Populations with Unknown Variances

Combining information from several independent normal populations to estimate a common mean parameter has applications in meta-analysis and is an important statistical problem. For this application, Gregurich and Broemeling (1997) and Tu (2012) concentrated on point estimation employing Bayesian techniques to infer about the common mean of two normal populations with unknown variances. In our study, we expand upon their investigation to encompass k normal populations with a common mean, incorporating a range of objective priors. Through the use of two examples, it is discovered that as the hyperparameter α under a Bayesian framework increases, the performance of the Bayesian technique also improves. IJSS, Vol. 24(2) Special, December, 2024, pp 81-94