{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T02:16:17Z","timestamp":1773972977938,"version":"3.50.1"},"reference-count":0,"publisher":"Informa UK Limited","issue":"2","license":[{"start":{"date-parts":[[1998,1,1]],"date-time":"1998-01-01T00:00:00Z","timestamp":883612800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics and Decision Sciences"],"published-print":{"date-parts":[[1998,1,1]]},"abstract":"<jats:p>In the classical decision theory framework, the loss is a function of the decision taken\nand the state of nature as represented by a parameter <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>\u03b8<\/mml:mi><\/mml:math>. Information about <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>\u03b8<\/mml:mi><\/mml:math> can be obtained\nvia observation of a random variable <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>X<\/mml:mi><\/mml:math>. In some situations however the loss will depend not\ndirectly on <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>\u03b8<\/mml:mi><\/mml:math> but on the observed value of another random variable <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>Y<\/mml:mi><\/mml:math> whose distribution depends\non <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>\u03b8<\/mml:mi><\/mml:math>. This adds an extra layer to the decision problem, and may lead to a wider choice of actions.\nIn particular there are now two sample sizes to choose, for <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>X<\/mml:mi><\/mml:math> and for <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>Y<\/mml:mi><\/mml:math>, leading to a range of\nbehaviours in the Bayes risk. We illustrate this with a problem arising from the cleanup of sites\ncontaminated with radioactive waste. We also discuss some computational approaches.<\/jats:p>","DOI":"10.1155\/s1173912698000054","type":"journal-article","created":{"date-parts":[[2007,3,8]],"date-time":"2007-03-08T07:44:28Z","timestamp":1173339868000},"page":"107-117","source":"Crossref","is-referenced-by-count":1,"title":["The predictive distribution in decision theory: a\ncase study"],"prefix":"10.1080","volume":"2","author":[{"given":"Geoff","family":"Jones","sequence":"first","affiliation":[{"name":"Institute of Information Sciences and Technology, College of Sciences, Massey University, New Zealand"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"301","container-title":["Journal of Applied Mathematics and Decision Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/archive\/1998\/678618.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/archive\/1998\/678618.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,8]],"date-time":"2024-08-08T14:22:55Z","timestamp":1723126975000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/ads\/1998\/678618\/abs\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,1,1]]},"references-count":0,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1998,1,1]]}},"alternative-id":["678618"],"URL":"https:\/\/doi.org\/10.1155\/s1173912698000054","relation":{},"ISSN":["1173-9126"],"issn-type":[{"value":"1173-9126","type":"print"}],"subject":[],"published":{"date-parts":[[1998,1,1]]}}}