{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,23]],"date-time":"2026-09-23T19:04:38Z","timestamp":1790190278984,"version":"4.1.0"},"reference-count":15,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[1964,7,1]],"date-time":"1964-07-01T00:00:00Z","timestamp":-173664000000},"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":[[1964,7,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>In the theory of statistical tolerance regions, as usually presented in frequentist terms, there are inherent difficulties of formulation, development and interpretation. The present paper re-examines the basic problem from a Bayesian point of view and suggests that such an approach provides a set of widely applicable, mathematically tractable tools, often more tailored to the requirements of users than the corresponding frequentist tools. For the one-dimensional case, Bayesian intervals are quoted for a number of standard distributions and prior densities, and the customary feature of a Bayesian analysis\u2014that special prior densities give rise to standard frequentist results\u2014is briefly demonstrated. A problem which seems to be of greater practical significance, namely the selection of an optimum tolerance region from a set of possible tolerance regions, is also investigated and the overwhelming advantages of the Bayesian approach are indicated.<\/jats:p>","DOI":"10.1111\/j.2517-6161.1964.tb00550.x","type":"journal-article","created":{"date-parts":[[2018,12,7]],"date-time":"2018-12-07T05:10:42Z","timestamp":1544159442000},"page":"161-175","source":"Crossref","is-referenced-by-count":58,"title":["Two Papers on the Comparison of Bayesian and Frequentist Approaches to Statistical Problems of Prediction: Bayesian Tolerance Regions"],"prefix":"10.1093","volume":"26","author":[{"given":"J.","family":"Aitchison","sequence":"first","affiliation":[{"name":"University of Liverpool"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2018,12,5]]},"reference":[{"key":"2024090921083361000_rssb00550-cit-0001","article-title":"Tolerance limits for normal distributions","volume-title":"Selected Techniques of Statistical Analysis","author":"Bowker","year":"1947"},{"key":"2024090921083361000_rssb00550-cit-0002","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1214\/aoms\/1177729081","article-title":"Non-parametric tolerance regions","volume":"24","author":"Fraser","year":"1953","journal-title":"Ann. math. 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B"}],"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.2517-6161.1964.tb00550.x","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/26\/2\/161\/49099549\/jrsssb_26_2_161.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/26\/2\/161\/49099549\/jrsssb_26_2_161.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,9]],"date-time":"2024-09-09T22:05:27Z","timestamp":1725919527000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/26\/2\/161\/7028123"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1964,7,1]]},"references-count":15,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2018,12,5]]},"published-print":{"date-parts":[[1964,7,1]]}},"URL":"https:\/\/doi.org\/10.1111\/j.2517-6161.1964.tb00550.x","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[1964,7]]},"published":{"date-parts":[[1964,7,1]]}}}