Bayesian Methods for Statistical Inference on the Common Mean from Multiple Data Sources

摘要

Combining studies or data from different sources for estimation of some related or common quantities has arisen in a number of applied problems. While there are myriad results on the development of various estimators of the common mean using classical/frequentist statistical approaches, there is lack of unifying rules and understanding of the statistical inference procedures such as confidence intervals or hypothesis testing. Indeed, if the variances are different and unknown, the inferential problem is notoriously difficult, and is related to the well-known Behrens-Fisher problem. This paper will show how Bayesian statistics provides a unifying tool for uncertainty analysis in the most general multi-laboratory and multiple methods problems. Software implementations will be discussed for facilicitating popularization of Bayesian methods among practical users.