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Probability is used in such a way that in general only bounds may be placed on the probabilities of given events, and probability systems of this kind are suggested both for sample information and for prior information. These systems are then combined using a specified rule. Illustrations are given for inferences about trinomial probabilities, and for inferences about a monotone sequence of binomial pi. Finally, some comments are made on the general class of models which produce upper and lower probabilities, and on the specific models which underlie the suggested inference procedures.<\/jats:p>","DOI":"10.1111\/j.2517-6161.1968.tb00722.x","type":"journal-article","created":{"date-parts":[[2018,12,7]],"date-time":"2018-12-07T00:23:42Z","timestamp":1544142222000},"page":"205-232","source":"Crossref","is-referenced-by-count":1802,"title":["A Generalization of Bayesian Inference"],"prefix":"10.1093","volume":"30","author":[{"given":"A. P.","family":"Dempster","sequence":"first","affiliation":[{"name":"Harvard University and London School of Economics"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2018,12,5]]},"reference":[{"key":"2024090920461868800_rssb00722-cit-0001","volume-title":"An Investigation of the Laws of Thought.","author":"Boole","year":"1854"},{"key":"2024090920461868800_rssb00722-cit-0002","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1214\/aoms\/1177699517","article-title":"New methods for reasoning towards posterior distributions based on sample data","volume":"37","author":"Dempster","year":"1966","journal-title":"Ann. Math. Statist."},{"key":"2024090920461868800_rssb00722-cit-0003","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1214\/aoms\/1177698950","article-title":"Upper and lower probabilities induced by a multivalued mapping","volume":"38","author":"Dempster","year":"1967","journal-title":"Ann. Math. 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A"}],"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2Fj.2517-6161.1968.tb00722.x","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/30\/2\/205\/49095334\/jrsssb_30_2_205.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/30\/2\/205\/49095334\/jrsssb_30_2_205.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,9]],"date-time":"2024-09-09T16:54:27Z","timestamp":1725900867000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/30\/2\/205\/7027004"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1968,7,1]]},"references-count":8,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2018,12,5]]},"published-print":{"date-parts":[[1968,7,1]]}},"URL":"https:\/\/doi.org\/10.1111\/j.2517-6161.1968.tb00722.x","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[1968,7]]},"published":{"date-parts":[[1968,7,1]]}}}