{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,8]],"date-time":"2026-10-08T07:29:31Z","timestamp":1791444571468,"version":"4.3.3"},"reference-count":23,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[1991,9,1]],"date-time":"1991-09-01T00:00:00Z","timestamp":683683200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1991,9,1]]},"abstract":"<jats:title>SUMMARY<\/jats:title>\n               <jats:p>A general procedure for computing Bayes factors for the comparison of arbitrary models is described, based on the use of the posterior mean of the likelihood under each model rather than the usual prior mean. The use of the posterior mean has several advantages, including reduced sensitivity to variations in the prior and the avoidance of the Lindley paradox in testing point null hypotheses. The frequency properties of the new procedure are evaluated in standard examples, and a non-standard example is analysed to show the considerable differences possible between prior and posterior means of the likelihood. Several different justifications of the procedure are given, and a non-Bayesian direct likelihood interpretation is described.<\/jats:p>","DOI":"10.1111\/j.2517-6161.1991.tb01812.x","type":"journal-article","created":{"date-parts":[[2018,12,7]],"date-time":"2018-12-07T07:06:35Z","timestamp":1544166395000},"page":"111-128","source":"Crossref","is-referenced-by-count":261,"title":["Posterior Bayes Factors"],"prefix":"10.1093","volume":"53","author":[{"given":"Murray","family":"Aitkin","sequence":"first","affiliation":[{"name":"Tel A viv University , Israel"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2018,12,5]]},"reference":[{"key":"2024090922051262200_rssb01812-cit-0001","volume-title":"Statistical Modelling in GLIM","author":"Aitkin","year":"1989"},{"key":"2024090922051262200_rssb01812-cit-0002","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-3678-8_36","article-title":"Likelihood analysis of a binomial sample size problem","volume-title":"Contributions to Probability and Statistics","author":"Aitkin","year":"1989"},{"key":"2024090922051262200_rssb01812-cit-0003","first-page":"267","article-title":"Information theory and the extension of the maximum likelihood principle","volume-title":"Proc. 2nd Int. 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Ass."},{"key":"2024090922051262200_rssb01812-cit-0007","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4899-2887-0","volume-title":"Theoretical Statistics.","author":"Cox","year":"1974"},{"key":"2024090922051262200_rssb01812-cit-0008","first-page":"335","article-title":"The direct use of likelihood for significance testing","volume-title":"Proc. Conf. 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Ass."},{"key":"2024090922051262200_rssb01812-cit-0017","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1093\/biomet\/75.2.223","article-title":"Inference for the binomial N parameter: A hierarchical Bayes approach","volume":"75","author":"Raftery","year":"1988","journal-title":"Biometrika"},{"key":"2024090922051262200_rssb01812-cit-0018","article-title":"A new model selection criterion","volume-title":"Research Report S-96.","author":"Raghunathan","year":"1984"},{"key":"2024090922051262200_rssb01812-cit-0019","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1214\/aos\/1176344136","article-title":"Estimating the dimension of a model","volume":"6","author":"Schwarz","year":"1978","journal-title":"Ann. Statist."},{"key":"2024090922051262200_rssb01812-cit-0020","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1080\/01621459.1982.10477809","article-title":"Lindley's paradox","volume":"77","author":"Shafer","year":"1982","journal-title":"J. Am. Statist. 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