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The Bayes statistic is based on the reference, Geisser\u2013Cornfield prior distribution which makes the posterior (discrete) distribution of the mean to be supported by the observed data with probabilities determined via the geometric means of the distances between data points. The maximum likelihood estimator coincides with the observation which has the maximal posterior probability. These procedures can be useful when measurement uncertainties are not reported or are misspecified.<\/jats:p>","DOI":"10.1111\/rssb.12227","type":"journal-article","created":{"date-parts":[[2017,2,9]],"date-time":"2017-02-09T12:26:58Z","timestamp":1486643218000},"page":"1601-1618","source":"Crossref","is-referenced-by-count":13,"title":["Estimation of the Common Mean from Heterogeneous Normal Observations with Unknown Variances"],"prefix":"10.1093","volume":"79","author":[{"given":"Andrew L.","family":"Rukhin","sequence":"first","affiliation":[{"name":"National Institute of Standards and Technology , Gaithersburg , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2017,2,9]]},"reference":[{"key":"2023022002194836400_rssb12227-cit-0001","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1111\/j.1740-9713.2016.00877.x","article-title":"Citizen science and statistics: playing a part","volume":"13","author":"Bain","year":"2016","journal-title":"Significance"},{"key":"2023022002194836400_rssb12227-cit-0002","first-page":"963","article-title":"Point and confidence estimation of a common mean and recovery of interblock information","volume":"2","author":"Brown","year":"1976","journal-title":"Ann. 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